We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this...We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.展开更多
We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as ...We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.展开更多
By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived.Based on the derivedsolita...By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived.Based on the derivedsolitary wave excitation,we obtain some special peakon excitations and fractal dromions in this short note.展开更多
Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary ...Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary waves like peakons,dromions,and compactons are investigated and some novel features or interesting behaviors are revealed.The results show that the interactions for peakon-dromion,compacton-dromion,and peakon-compacton may be completely nonelastic or completely elastic.展开更多
Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solu...Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed.展开更多
A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the(2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting ...A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the(2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting appropriate functions,we discuss the completely elastic head-on collision between two dromion-lattices,non-completely elastic "chase and collision" between two multi-dromion-pairs and completely non-elastic interaction phenomenon between anti-dromion and dromion-pair.展开更多
By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Boiti-Leon-Pempinelli （BLP） system is derived. Based on the derived sol...By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Boiti-Leon-Pempinelli （BLP） system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated.展开更多
Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidro...Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidromion solution, multi-peakon and multi-compacton solution, for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are found by selecting appropriate functions. These new structures exhibit novel interaction features. Their interaction behavior is very similar to the completely nonelastic collisions between two classical particles.展开更多
The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations.In this paper,we use a new form of variable separation to study novel soliton molecules and thei...The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations.In this paper,we use a new form of variable separation to study novel soliton molecules and their interactions in(2+1)-dimensional potential Boiti–Leon-Manna–Pempinelli equation.Dromion molecules,ring molecules,lump molecules,multi-instantaneous molecules,and their interactions are obtained.Then we draw corresponding images with maple software to study their dynamic behavior.展开更多
文摘We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
文摘We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ05010
文摘By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general (2+1)-dimensional Korteweg de Vries system (GKdV) are derived.Based on the derivedsolitary wave excitation,we obtain some special peakon excitations and fractal dromions in this short note.
文摘Starting from the known variable separation excitations of a(2 + 1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system,rich coherent structures can be derived.The interactions among different types of solitary waves like peakons,dromions,and compactons are investigated and some novel features or interesting behaviors are revealed.The results show that the interactions for peakon-dromion,compacton-dromion,and peakon-compacton may be completely nonelastic or completely elastic.
基金supported by National Natural Science Foundation of China under Grant No.10272071the Natural Science Foundation of Zhejiang Province under Grant No.Y606049
文摘Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed.
基金Supported by the National Natural Science Foundation of China under Grant No. 11005092the Program for Innovative Research Team of Young Teachers under Grant No. 2009RC01Undergraduate Innovative Base of Zhejiang Agriculture and Forestry University,the Zhejiang Province Undergraduate Scientific and Technological Innovation Project under Grant No. 2012R412018
文摘A modified mapping method is used to obtain variable separation solution with two arbitrary functions of the(2+1)-dimensional Broer-Kaup-Kupershmidt equation.Based on the variable separation solution and by selecting appropriate functions,we discuss the completely elastic head-on collision between two dromion-lattices,non-completely elastic "chase and collision" between two multi-dromion-pairs and completely non-elastic interaction phenomenon between anti-dromion and dromion-pair.
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y6100257, Y6110140, and Y6090681)the Natural Science Foundation of Zhejiang Lishui University, China (Grant Nos. KZ09005 and KY08003)
文摘By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Boiti-Leon-Pempinelli （BLP） system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated.
文摘Starting from the variable separation solution obtained by using the extended homogenous balance method,a new class of combined structures, such as multi-peakon and multi-dromion solution, multi-compacton and multidromion solution, multi-peakon and multi-compacton solution, for the (2+1)-dimensional Nizhnik-Novikov-Veselov equation are found by selecting appropriate functions. These new structures exhibit novel interaction features. Their interaction behavior is very similar to the completely nonelastic collisions between two classical particles.
基金the National Natural Science Foundation of China(Grant Nos.11371086,11671258,and 11975145)the Fund of Science and Technology Commission of Shanghai Municipality(Grant No.13ZR1400100)。
文摘The method of variable separation has always been regarded as a crucial method for solving nonlinear evolution equations.In this paper,we use a new form of variable separation to study novel soliton molecules and their interactions in(2+1)-dimensional potential Boiti–Leon-Manna–Pempinelli equation.Dromion molecules,ring molecules,lump molecules,multi-instantaneous molecules,and their interactions are obtained.Then we draw corresponding images with maple software to study their dynamic behavior.
