Objective To retrospectively analyze the relationship between curve types and clinical results in surgical treatment of scoliosis in patients with neurofibromatosis type 1 (NF-1). Methods Forty-five patients with scol...Objective To retrospectively analyze the relationship between curve types and clinical results in surgical treatment of scoliosis in patients with neurofibromatosis type 1 (NF-1). Methods Forty-five patients with scoliosis resulting from NF-1 were treated surgically from 1984 to 2002. Mean age at operation was 14.2 years. There were 6 nondystrophic curves and 39 dystrophic curves depended on their radiographic featu- res. According to their apical vertebrae location, the dystrophic curves were divided into three subgroups: thoracic curve (apical vertebra at T8 or above), thoracolumbar curve (apical vertebra below T8 and above L1), and lumber curve (apical vertebra at L1 and below). Posterior spine fusion, combined anterior and posterior spine fusion were administrated based on the type and location of the curves. Mean follow-up was 6.8 years. Clinical and radiological manifestations were investigated and results were assessed. Results Three patients with muscle weakness of low extremities recovered entirely. Two patients with dystrophic lum- bar curve maintained their low back pain the same as preoperatively. The mean coronal and sagittal Cobb’s angle in nondy- strophic curves was 80.3o and 61.7o before operation, 30.7o and 36.9o after operation, and 32.9o and 42.1o at follow-up, respectively. In dystrophic thoracic curves, preoperative Cobb’s angle in coronal and sagittal plane was 96.5o and 79.8o, postoperative 49.3o and 41.7o, follow-up 54.1o and 45.3o, respectively. In thoracolumbar curves, preoperative Cobb’s angle in coronal and sagittal plane was 75.0o and 47.5o, postoperative 31.2o and 22.8o, follow-up 37.5o and 27.8o, respectively. In lumbar curves preoperative Cobb’s angle in coronal plane was 55.3o, postoperative 19.3o, and follow-up 32.1o. Six patients with dystrophic curves had his or her curve deteriorated more than 10 degrees at follow-up. Three of them were in the thoracic subgroup and their kyphosis was larger than 95 degrees, and three in lumbar subgroup. Hardware failure occurred in 3 cases. Six patients had 7 revision procedures totally. Conclusions Posterior spinal fusion is effective for most dystrophic thoracic curves in patients whose kyphosis is less than 95 degrees. Combined anterior and posterior spinal fusion is stronger recommended for patients whose kyphosis is larger than 95 degrees and those whose apical vertebra is located below T8. Patients should be informed that repeated spine fusion might be necessary even after combined anterior and posterior spine fusion.展开更多
OBJECTIVE To explore the relationship between multimarker detection of MAGE-1,MAGE-3 and AFP mRNAs in the peripheral blood of patients with hepatocellular carcinoma and micrometastasis using a realtime quantitative-PC...OBJECTIVE To explore the relationship between multimarker detection of MAGE-1,MAGE-3 and AFP mRNAs in the peripheral blood of patients with hepatocellular carcinoma and micrometastasis using a realtime quantitative-PCR(real-time Q-PCR)assay. METHODS Peripheral blood samples were obtained from control subjects and 86 patients with hepatocellular carcinoma (HCC).Real-time Q-PCR was used to detect MAGE-1,MAGE-3, and AFP mRNAs in the blood cells. RESULTS In 86 tumor specimens,the positivity for MAGE-1, MAGE-3,and AFP genes was respectively 34.9%(30/86),60.5% (52/86)and 69.8%(60/86).All specimens expressed at least one marker.MAGE-1,MAGE-3,and AFP transcripts were detected respectively in 12(14.0%),18(20.1%)and 29(33.7%)of the 86 blood specimens from hepatocellular carcinoma patients,while 45 specimens(52.3%)were positive for at least one marker.In addition,MAGE-1,MAGE-3 and AFP gene transcripts were not detected in any peripheral blood specimens from 25 chronic liver disease patients and 28 normal healthy volunteers.The positive rate correlated with the TNM clinical stages,extrahepatic metastasis and portal vein carcinothrombosis(P<0.05).No correlation was found between tumor size,tumor number, differentiation,serum a-fetoprotein(AFP)and the positive rate. CONCLUSION Our results indicate that a multimarker real- time Q-PCR assay with cancer-specific markers such as MAGE-1 and MAGE-3 in combination with a hepatocyte-specific AFP marker may be a promising diagnostic tool for monitoring hepatocellular carcinoma patients with better sensitivity and specificity.展开更多
Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the (2+1)- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the gr...Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the (2+1)- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou's direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.展开更多
Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Backlund transformation and a number of ...Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Backlund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass & function. Some of them are novel.展开更多
Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in...Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.展开更多
In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+ 1 )-dimensional Nizhnik-Novikov-Veselov equati...In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+ 1 )-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.展开更多
With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) ...With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.展开更多
Objective: To establish angiogenesis model of xenografts of lung cancer cell in nude mouse and investigate the expression of the neuropilin-1 (NRP-1) protein in tumors and its role in progression and angiogenesis o...Objective: To establish angiogenesis model of xenografts of lung cancer cell in nude mouse and investigate the expression of the neuropilin-1 (NRP-1) protein in tumors and its role in progression and angiogenesis of lung cancer. Methods: Human lung adenocarcinoma cells A549 were analyzed for the expression of vascular endothelial growth factor- 165 (VEGF16s) mRNA using RT-PCR in vitro. Two groups of nude mice were subcutaneously inoculated with A549 at different tumor-loading time. Two groups of xenografts were identified by hematoxylin and eosin (HE) staining, their microvessel density (MVD) were analyzed meanwhile. Two groups were analyzed for the expression of NRP-1 protein and their mean absorbency by using immunohistochemistry and automatic image analysis system respectively. Results: A549 expressed VEGF165 mRNA, and xenografts of A549 in nude mice were successfully established and confirmed by HE staining. The atypia of cancer cells and angiogenesis were occurred in two groups. Two groups of MVD were 13.06 ± 1.58, 23.61 ± 3.11 (vessels/mm^2) (P 〈 0.01). NRP-1 protein was expressed in cytoplasm of vascular endothelium cells and partial tumor cells. Two groups of mean absorbency of NRP-1 were 0.1095 ± 0.0228, 0.1784 ± 0.0151 (P 〈 0.01). Conclusion: The angiogenesis models of xenografts in nude mice with lung cancer cell A549 expressing VEGF165 mRNA at different tumor-loading times were established successfully. The expression of NRP-1 protein and MVD were increased with the tumor progression. Our results demonstrate that NRP-1 protein in tung cancer is related to angiogenesis.展开更多
Special solution of the (2+1)-dimensional Sawada Kotera equation is decomposed into three (0+1)- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve....Special solution of the (2+1)-dimensional Sawada Kotera equation is decomposed into three (0+1)- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy.展开更多
The molecular modifications of Herpes Simplex Virus Type I (HSV-1) proteins represented by acetylation and phosphorylation are essential to its biological functions. The cellular chromatin-remodeling/ assembly is in...The molecular modifications of Herpes Simplex Virus Type I (HSV-1) proteins represented by acetylation and phosphorylation are essential to its biological functions. The cellular chromatin-remodeling/ assembly is involved in HSV-1 associated gene transcriptional regulation in human cells harboring HSV-1 lytic or latent infections. Further investigation on these biological events would provide a better understanding of the mechanisms of HSV-1 viral gene transcriptional regulation展开更多
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. The...In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.展开更多
In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polyno...In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.展开更多
Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we wi...Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we will use the technique of the vertex insertion on l connected ( l=k or k+1,k≥2 ) claw free graphs to provide a unified proof for G to be hamiltonian or 1 hamiltonian, the sufficient conditions are expressed by the inequality concerning ∑ki=0N(Y i) and n(Y) for each essential set Y={y 0,y 1,...,y k} of G , where Y i={y i,y i-1 ,...,y i-(b-1) }Y for i∈{0,1,...,k} (the subscriptions of y j ’s will be taken modulo k+1 ), b ( 0【b【k+1 ) is an integer, and n(Y)={v∈V(G): dist (v,Y)≤2 }.展开更多
The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trig...The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort.展开更多
Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generali...Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the (2+1)-dimentional breaking soliton equation. As a result, we successfully obtain some new and more general solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sampler the properties of some soliton solutions for the breaking soliton equation are shown by some figures. Our method can also be applied to other partial differential equations.展开更多
文摘Objective To retrospectively analyze the relationship between curve types and clinical results in surgical treatment of scoliosis in patients with neurofibromatosis type 1 (NF-1). Methods Forty-five patients with scoliosis resulting from NF-1 were treated surgically from 1984 to 2002. Mean age at operation was 14.2 years. There were 6 nondystrophic curves and 39 dystrophic curves depended on their radiographic featu- res. According to their apical vertebrae location, the dystrophic curves were divided into three subgroups: thoracic curve (apical vertebra at T8 or above), thoracolumbar curve (apical vertebra below T8 and above L1), and lumber curve (apical vertebra at L1 and below). Posterior spine fusion, combined anterior and posterior spine fusion were administrated based on the type and location of the curves. Mean follow-up was 6.8 years. Clinical and radiological manifestations were investigated and results were assessed. Results Three patients with muscle weakness of low extremities recovered entirely. Two patients with dystrophic lum- bar curve maintained their low back pain the same as preoperatively. The mean coronal and sagittal Cobb’s angle in nondy- strophic curves was 80.3o and 61.7o before operation, 30.7o and 36.9o after operation, and 32.9o and 42.1o at follow-up, respectively. In dystrophic thoracic curves, preoperative Cobb’s angle in coronal and sagittal plane was 96.5o and 79.8o, postoperative 49.3o and 41.7o, follow-up 54.1o and 45.3o, respectively. In thoracolumbar curves, preoperative Cobb’s angle in coronal and sagittal plane was 75.0o and 47.5o, postoperative 31.2o and 22.8o, follow-up 37.5o and 27.8o, respectively. In lumbar curves preoperative Cobb’s angle in coronal plane was 55.3o, postoperative 19.3o, and follow-up 32.1o. Six patients with dystrophic curves had his or her curve deteriorated more than 10 degrees at follow-up. Three of them were in the thoracic subgroup and their kyphosis was larger than 95 degrees, and three in lumbar subgroup. Hardware failure occurred in 3 cases. Six patients had 7 revision procedures totally. Conclusions Posterior spinal fusion is effective for most dystrophic thoracic curves in patients whose kyphosis is less than 95 degrees. Combined anterior and posterior spinal fusion is stronger recommended for patients whose kyphosis is larger than 95 degrees and those whose apical vertebra is located below T8. Patients should be informed that repeated spine fusion might be necessary even after combined anterior and posterior spine fusion.
基金This work was supported by a grant from the Tianjin Natural Science Foundation of China(No.023610811)
文摘OBJECTIVE To explore the relationship between multimarker detection of MAGE-1,MAGE-3 and AFP mRNAs in the peripheral blood of patients with hepatocellular carcinoma and micrometastasis using a realtime quantitative-PCR(real-time Q-PCR)assay. METHODS Peripheral blood samples were obtained from control subjects and 86 patients with hepatocellular carcinoma (HCC).Real-time Q-PCR was used to detect MAGE-1,MAGE-3, and AFP mRNAs in the blood cells. RESULTS In 86 tumor specimens,the positivity for MAGE-1, MAGE-3,and AFP genes was respectively 34.9%(30/86),60.5% (52/86)and 69.8%(60/86).All specimens expressed at least one marker.MAGE-1,MAGE-3,and AFP transcripts were detected respectively in 12(14.0%),18(20.1%)and 29(33.7%)of the 86 blood specimens from hepatocellular carcinoma patients,while 45 specimens(52.3%)were positive for at least one marker.In addition,MAGE-1,MAGE-3 and AFP gene transcripts were not detected in any peripheral blood specimens from 25 chronic liver disease patients and 28 normal healthy volunteers.The positive rate correlated with the TNM clinical stages,extrahepatic metastasis and portal vein carcinothrombosis(P<0.05).No correlation was found between tumor size,tumor number, differentiation,serum a-fetoprotein(AFP)and the positive rate. CONCLUSION Our results indicate that a multimarker real- time Q-PCR assay with cancer-specific markers such as MAGE-1 and MAGE-3 in combination with a hepatocyte-specific AFP marker may be a promising diagnostic tool for monitoring hepatocellular carcinoma patients with better sensitivity and specificity.
基金the State Key Basic Research Program of China under Grant No.2004CB318000
文摘Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the (2+1)- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou's direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.
基金National Natural Science Foundation of China under Grant No.10761005the Natural Science Foundation of Inner Mongolia under Grant No.200607010104
文摘Using the truncated Painleve expansion, symbolic computation, and direct integration technique, we study analytic solutions of (2+1)-dimensional Boussinesq equation. An auto-Backlund transformation and a number of exact solutions of this equation have been found. The set of solutions include solitary wave solutions, solitoff solutions, and periodic solutions in terms of elliptic Jacobi functions and Weierstrass & function. Some of them are novel.
基金National Natural Science Foundation of China under Grant No.10272071the Natural Science Foundation of Zhejiang Province under Grant No.Y504111the Scientific Research Foundation of Huzhou University
文摘Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional breaking soliton system. By introducing Jacobi elliptic functions in the seed solution, two families of doubly periodic propagating wave patterns are derived. We investigate these periodic wave solutions with different modulus m selections, many important and interesting properties are revealed. The interaction of Jabcobi elliptic function waves are graphically considered and found to be nonelastic.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000 .
文摘In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the (2+ 1 )-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y606128 and Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant Nos.FC06001 and QN06009
文摘With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.
基金Province Science and Technology of Hubei Key Program Foundation (No. 2003AA301C05)
文摘Objective: To establish angiogenesis model of xenografts of lung cancer cell in nude mouse and investigate the expression of the neuropilin-1 (NRP-1) protein in tumors and its role in progression and angiogenesis of lung cancer. Methods: Human lung adenocarcinoma cells A549 were analyzed for the expression of vascular endothelial growth factor- 165 (VEGF16s) mRNA using RT-PCR in vitro. Two groups of nude mice were subcutaneously inoculated with A549 at different tumor-loading time. Two groups of xenografts were identified by hematoxylin and eosin (HE) staining, their microvessel density (MVD) were analyzed meanwhile. Two groups were analyzed for the expression of NRP-1 protein and their mean absorbency by using immunohistochemistry and automatic image analysis system respectively. Results: A549 expressed VEGF165 mRNA, and xenografts of A549 in nude mice were successfully established and confirmed by HE staining. The atypia of cancer cells and angiogenesis were occurred in two groups. Two groups of MVD were 13.06 ± 1.58, 23.61 ± 3.11 (vessels/mm^2) (P 〈 0.01). NRP-1 protein was expressed in cytoplasm of vascular endothelium cells and partial tumor cells. Two groups of mean absorbency of NRP-1 were 0.1095 ± 0.0228, 0.1784 ± 0.0151 (P 〈 0.01). Conclusion: The angiogenesis models of xenografts in nude mice with lung cancer cell A549 expressing VEGF165 mRNA at different tumor-loading times were established successfully. The expression of NRP-1 protein and MVD were increased with the tumor progression. Our results demonstrate that NRP-1 protein in tung cancer is related to angiogenesis.
基金The project supported by the Special Funds for Major State Basic Research Project under Grant No.G2000077301
文摘Special solution of the (2+1)-dimensional Sawada Kotera equation is decomposed into three (0+1)- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy.
基金National Natural Science Foundation of China (30670094,30700028)
文摘The molecular modifications of Herpes Simplex Virus Type I (HSV-1) proteins represented by acetylation and phosphorylation are essential to its biological functions. The cellular chromatin-remodeling/ assembly is involved in HSV-1 associated gene transcriptional regulation in human cells harboring HSV-1 lytic or latent infections. Further investigation on these biological events would provide a better understanding of the mechanisms of HSV-1 viral gene transcriptional regulation
基金The project supported by National Natural Science Foundation of China undcr Grant No. 10172056 .
文摘In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.
文摘In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.
文摘Let G be a graph, an independent set Y in G is called an essential independent set (or essential set for simplicity), if there is {y 1,y 2} Y such that dist (y 1,y 2)=2. In this paper, we will use the technique of the vertex insertion on l connected ( l=k or k+1,k≥2 ) claw free graphs to provide a unified proof for G to be hamiltonian or 1 hamiltonian, the sufficient conditions are expressed by the inequality concerning ∑ki=0N(Y i) and n(Y) for each essential set Y={y 0,y 1,...,y k} of G , where Y i={y i,y i-1 ,...,y i-(b-1) }Y for i∈{0,1,...,k} (the subscriptions of y j ’s will be taken modulo k+1 ), b ( 0【b【k+1 ) is an integer, and n(Y)={v∈V(G): dist (v,Y)≤2 }.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘The generalized transformation method is utilized to solve three-dimensional Nizhnik-Novikov-Veselov equation and construct a series of new exact solutions including kink-shaped and bell-shaped soliton solutions, trigonometric function solutions, and Jacobi elliptic doubly periodic solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh methods and Jacobi function method, the method we used here gives more general exact solutions without much extra effort.
基金The project supported partially by the State Key Basic Research Program of China under Grant No. 2004 CB 318000The authors would like to thank the referee for his/her valuable suggestions.
文摘Making use of a new generalized ansatz, we present a new generalized extended F-expansion method for constructing the exact solutions of nonlinear partial differential equations in a unified way. Applying the generalized method with the aid of Maple, we consider the (2+1)-dimentional breaking soliton equation. As a result, we successfully obtain some new and more general solutions including Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, and so on. As an illustrative sampler the properties of some soliton solutions for the breaking soliton equation are shown by some figures. Our method can also be applied to other partial differential equations.