For a special coupled Korteweg de Vries （KdV） system, its similarity solutions and reduction equations are obtained by the Clarkson and Kruskal＇s direct method. In addition, its new explicit soliton solutions and t...For a special coupled Korteweg de Vries （KdV） system, its similarity solutions and reduction equations are obtained by the Clarkson and Kruskal＇s direct method. In addition, its new explicit soliton solutions and traveling wave solutions are found by the deformation and mapping method.展开更多
New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solu...New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.展开更多
With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov system （NNV） is d...With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov system （NNV） is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the （2＋1）-dimensional NNV system.展开更多
In this paper, we extend the mapping approach to the N-order Schrodinger equation. In terms of the extended mapping approach, new families of variable separation solutions with some arbitrary functions are derived.
Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitra...Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitrary functions is derived.展开更多
A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the non...A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.展开更多
基金Supported by Natural Science Foundations of Jiangxi Province under Grant Nos. 2008GZS0045 and 2009GZW0026
文摘For a special coupled Korteweg de Vries （KdV） system, its similarity solutions and reduction equations are obtained by the Clarkson and Kruskal＇s direct method. In addition, its new explicit soliton solutions and traveling wave solutions are found by the deformation and mapping method.
文摘New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.
基金supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y604106the Scientific Research Foundation of Zhejiang Provincial Education Department under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ08001
文摘With the help of an improved mapping approach and a linear-variable-separation approach, a new family of exact solutions with arbitrary functions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov system （NNV） is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations for the （2＋1）-dimensional NNV system.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005
文摘In this paper, we extend the mapping approach to the N-order Schrodinger equation. In terms of the extended mapping approach, new families of variable separation solutions with some arbitrary functions are derived.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ04008
文摘Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitrary functions is derived.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675084 and 11435005Ningbo Natural Science Foundation under Grant No.2015A610159+1 种基金granted by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No.xkzwl1502sponsored by K.C.Wong Magna Fund in Ningbo University
文摘A coupled KdV equation is studied in this manuscript. The exact solutions, such as the periodic wave solutions and solitary wave solutions by means of the deformation and mapping approach from the solutions of the nonlinear φ4 model are given. Using the symmetry theory, the Lie point symmetries and symmetry reductions of the coupled KdV equation are presented. The results show that the coupled KdV equation possesses infinitely many symmetries and may be considered as an integrable system. Also, the Palnleve test shows the coupled KdV equation possesses Palnleve property. The Backlund transformations of the coupled KdV equation related to Palnleve property and residual symmetry are shown.
