Journal ArticleDOI
Multiple-soliton solutions for the kp equation by hirota’s bilinear method and by the tanh–coth method
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TLDR
The Hirota’s direct method combined with the simplified version of this method is used to determine the N-soliton solutions for the Kadomtsev–Petviashvili (KP) equation.About:
This article is published in Applied Mathematics and Computation.The article was published on 2007-07-01. It has received 238 citations till now. The article focuses on the topics: Kadomtsev–Petviashvili equation.read more
Citations
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Asymptotic Methods for Solitary Solutions and Compactons
TL;DR: In this paper, a review of the variational approach, the Hamiltonian approach, variational iteration method, the homotopy perturbation method, parameter expansion method, Yang-Laplace transform, and Yang-Fourier transform is presented.
Journal ArticleDOI
The Hirota’s direct method for multiple-soliton solutions for three model equations of shallow water waves
TL;DR: The Hirota bilinear method is used to determine multiple-soliton solutions of sech-squared type for three model equations for shallow water waves that are completely integrable.
Journal ArticleDOI
One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada–Kotera equation
TL;DR: In this article, a single-and double-soliton rational solution for the VcSK model is presented. But the model is not considered in this paper, as the authors assume that the velocity, the amplitude and the shape of the wave cannot be affected by variable coefficients, and there is an inelastic collision (the collision that makes change in amplitude of the soliton waves and shifts in their trajectories).
Journal ArticleDOI
An efficient algorithm to construct multi-soliton rational solutions of the (2+ 1)-dimensional KdV equation with variable coefficients
TL;DR: An efficient algorithm to construct multi-soliton rational solutions of the Korteweg–de Vries equation with time-dependent coefficients with wider applicability for handling many other nonlinear evolution equations in different branches of science is presented.
Journal ArticleDOI
On the integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation
TL;DR: In this paper, the complete integrability of the generalized variable-coefficient Kadomtsev-Petviashvili (vc-KP) equation under an integrable constraint condition is investigated.
References
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Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Journal ArticleDOI
Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons
TL;DR: An exact solution for the Korteweg-de Vries equation for the case of multiple collisions of $N$ solitons with different amplitudes was obtained in this paper, which is the only known exact solution.
Book
The direct method in soliton theory
TL;DR: In this paper, Bilinearization of soliton equations is discussed and the Backlund transformation is used to transform the soliton equation into a linear combination of determinants and pfaffians.
Journal ArticleDOI
Exact envelope‐soliton solutions of a nonlinear wave equation
TL;DR: In this article, exact N-envelope-soliton solutions have been obtained for the following nonlinear wave equation, where α, β, γ and δ are real positive constants with the relation αβ = γδ.
Journal ArticleDOI
The tanh method: I. Exact solutions of nonlinear evolution and wave equations
Willy Malfliet,Willy Hereman +1 more
TL;DR: In this article, a systemized version of the tanh method is used to solve particular evolution and wave equations, where the boundary conditions are implemented in this expansion, and the associated velocity can then be determined a priori, provided the solution vanishes at infinity.
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