n-soliton-like solutions of three non-isospectral equations, the non-isospectral mKdV equation, the non-isospectral sine-Gordon equation and the non-isospectral nonlinear Schrdinger equation were obtained by using the...n-soliton-like solutions of three non-isospectral equations, the non-isospectral mKdV equation, the non-isospectral sine-Gordon equation and the non-isospectral nonlinear Schrdinger equation were obtained by using the Hirota method.展开更多
By bilinear approach we derive N-soliton-like solutions for a variable coefficient KdV equation with some x-dependent coefficients. This equation can be considered as a non-isospectral variable coefficient KdV equatio...By bilinear approach we derive N-soliton-like solutions for a variable coefficient KdV equation with some x-dependent coefficients. This equation can be considered as a non-isospectral variable coefficient KdV equation. Solutions in Hirota’s form and Wronskian form are given, respectively.展开更多
This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Ca...This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.展开更多
Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fraction...Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fractional breaking soliton equation is derived from the reduction of the linear spectral problem associated with the local fractional non-isospectral self-dual Yang-Mills equations.More specifically,the employed linear spectral problem is first reduced to the(2+1)-dimensional local fractional zero-curvature equation through variable transformations.Based on the reduced local fractional zero-curvature equation,the fractional breaking soliton equation is then constructed by the method of undetermined coefficients.This paper shows that some other local fractional models can be obtained by generalizing the existing methods of generating nonlinear partial differential equations with integer orders.展开更多
文摘n-soliton-like solutions of three non-isospectral equations, the non-isospectral mKdV equation, the non-isospectral sine-Gordon equation and the non-isospectral nonlinear Schrdinger equation were obtained by using the Hirota method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.10371070, 10671121)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘By bilinear approach we derive N-soliton-like solutions for a variable coefficient KdV equation with some x-dependent coefficients. This equation can be considered as a non-isospectral variable coefficient KdV equation. Solutions in Hirota’s form and Wronskian form are given, respectively.
基金supported by the National Natural Science Foundation of China(No.12271334).
文摘This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.
基金Liaoning BaiQianWan Talents Program of China(2019)National Natural Science Foundation of China(No.11547005)Natural Science Foundation of Education Department of Liaoning Province of China(2020)。
文摘Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fractional breaking soliton equation is derived from the reduction of the linear spectral problem associated with the local fractional non-isospectral self-dual Yang-Mills equations.More specifically,the employed linear spectral problem is first reduced to the(2+1)-dimensional local fractional zero-curvature equation through variable transformations.Based on the reduced local fractional zero-curvature equation,the fractional breaking soliton equation is then constructed by the method of undetermined coefficients.This paper shows that some other local fractional models can be obtained by generalizing the existing methods of generating nonlinear partial differential equations with integer orders.