Journal ArticleDOI
Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method
TLDR
In this article, the persistence of the solitary wave solution for the singularly perturbed higher-order KdV equation is investigated by using the geometric singular perturbation theory and dynamical systems approach when the perturbations parameter is suitably small.Abstract:
In this paper, we are concerned with a singularly perturbed higher-order KdV equation, which is considered as a paradigm in nonlinear science and has many applications in weakly nonlinear and weakly dispersive physical systems. Based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of the solitary wave solution for the singularly perturbed KdV equation is investigated by using the geometric singular perturbation theory and dynamical systems approach when the perturbation parameter is suitably small.read more
Citations
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Journal ArticleDOI
New solitary wave solutions in a perturbed generalized BBM equation
TL;DR: In this paper, the singular perturbation theory was used to detect new solitary wave solutions in a perturbed generalized Benjamin-Bona-Mahony (BBM) equation by the explicit calculation of the associated Melnikov integrals.
Journal ArticleDOI
A New Type of Solitary Wave Solution of the mKdV Equation Under Singular Perturbations
TL;DR: This work examines the solitary wave solutions of the mKdV equation with small singular perturbations through a combination of geometric singular perturbedation theory and Melnikov’s mKDV equation.
Journal ArticleDOI
Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation.
TL;DR: The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations and may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines.
Journal ArticleDOI
New type of solitary wave solution with coexisting crest and trough for a perturbed wave equation
TL;DR: In this article, the perturbed mK(3,1) equation is restudied to further explore the dynamics of solitary wave solutions by combining the geometric singular perturbation theorem and bifurcation analysis.
Journal ArticleDOI
Traveling waves in a generalized nonlinear dispersive–dissipative equation
Xiaohui Shang,Zengji Du +1 more
TL;DR: In this paper, the authors considered the existence of traveling waves in a generalized nonlinear dispersive-dissipative equation and constructed a locally invariant manifold for the associated traveling wave equation.
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
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Journal ArticleDOI
XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
D. J. de Korteweg,G. de Vries +1 more
TL;DR: In this article, the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves were discussed, and a new model of long wave propagation was proposed.
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