In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we o...In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we obtain the conservation laws of the Gardner equation,Landau-Ginzburg-Higgs equation and Hirota-Satsuma equation,respectively.展开更多
In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique...In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique.Considering the Lie invariance condition,we find the symmetry generators.The pro-posed model yields eight-dimensional Lie algebra.Moreover,an optimal system of sub-algebras is com-puted,and similarity reductions are made.The considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave solutions.These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton solutions.The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.展开更多
In this paper, the bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the...In this paper, the bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the mapping and deformation relations. In the case of two-fermionic-parameter bosonization procedure, we provide a special solution in the form of Jacobian elliptic functions. Meanwhile, we discuss and formally derive traveling wave solutions of N fermionic parameters bosonization procedure. This technique can also be applied to treat the N = 1 supersymmetry KdV and mKdV systems which are obtained in two limiting cases.展开更多
基金funded by the National Natural Science Foundation of China(Grant Nos.12371256&11971475)。
文摘In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we obtain the conservation laws of the Gardner equation,Landau-Ginzburg-Higgs equation and Hirota-Satsuma equation,respectively.
基金The authors would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project R-2022-178.
文摘In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique.Considering the Lie invariance condition,we find the symmetry generators.The pro-posed model yields eight-dimensional Lie algebra.Moreover,an optimal system of sub-algebras is com-puted,and similarity reductions are made.The considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave solutions.These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton solutions.The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.
基金supported by the Natural Science Foundation of Inner Mongolia(Grant No.2009MS0108)the Natural Science Foundation(Grant No ZRYB08017)the Initial Fundingof Scientific Research Project for Ph.D of Inner Mongolia Normal University~~
文摘In this paper, the bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the mapping and deformation relations. In the case of two-fermionic-parameter bosonization procedure, we provide a special solution in the form of Jacobian elliptic functions. Meanwhile, we discuss and formally derive traveling wave solutions of N fermionic parameters bosonization procedure. This technique can also be applied to treat the N = 1 supersymmetry KdV and mKdV systems which are obtained in two limiting cases.
