Book ChapterDOI
Solitons, Nonlinear Evolution Equations and Inverse Scattering: References
M. A. Ablowitz,Peter A. Clarkson +1 more
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The article was published on 1991-01-01. It has received 1213 citations till now. The article focuses on the topics: Inverse scattering transform & Inverse scattering problem.read more
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Variational iteration method for solving Burger's and coupled Burger's equations
M.A. Abdou,A.A. Soliman +1 more
TL;DR: In this article, He's variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials, and the solutions of Burger's equation and coupled Burger's equations are exactly obtained.
Journal ArticleDOI
Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation
TL;DR: In this paper, a detailed study of the inverse scattering transform of the non-local nonlinear Schrodinger (NLS) equation is carried out and key symmetries of the eigenfunctions and scattering data and conserved quantities are obtained.
Journal ArticleDOI
Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation
Xing Lü,Wen-Xiu Ma,Wen-Xiu Ma +2 more
TL;DR: In this article, two classes of lump solutions to the dimensionally reduced equations in (2+1)-dimensions are derived, respectively, by searching for positive quadratic function solutions to associated bilinear equations.
Journal ArticleDOI
Mixed lump-kink solutions to the BKP equation
TL;DR: By using the Hirota bilinear form of the (2+1)-dimensional BKP equation, ten classes of interaction solutions between lumps and kinks are constructed through Maple symbolic computations beginning with a linear combination ansatz.
Journal ArticleDOI
Lump solutions to dimensionally reduced $$\varvec{p}$$ p -gKP and $$\varvec{p}$$ p -gBKP equations
TL;DR: Based on generalized bilinear forms, lump solutions, rationally localized in all directions in the space, to dimensionally reduced p-gKP and P-gBKP equations in (2+1)-dimensions are computed through symbolic computation with Maple as discussed by the authors.