Cusp Soliton of a New Integrable Nonlinear Evolution Equation
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This article is published in Progress of Theoretical Physics.The article was published on 1980-12-01 and is currently open access. It has received 113 citations till now. The article focuses on the topics: sine-Gordon equation & Soliton.read more
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Nonlinear Partial Differential Equations for Scientists and Engineers
TL;DR: The Third edition of the Third Edition of as discussed by the authors is the most complete and complete version of this work. But it does not cover the first-order nonlinear Equations and their applications.
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A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
TL;DR: In this article, a Backlund transformation both in bilinear and in ordinary form for the transformed generalised Vakhnenko equation (GVE) is derived, and an inverse scattering problem is formulated; it has a third-order eigenvalue problem.
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The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
TL;DR: In this article, the authors investigated the geometry of soliton-like solutions for integrable nonlinear equations and obtained new solutions such as solitons with quasiperiodic background, billiard, and n-peakon solutions and complex angle representations for them.
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The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type
TL;DR: In this paper, an algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of N-component systems of nonlinear evolution equations.
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Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I. Compactions and peakons
Yi A. Li,Peter J. Olver +1 more
TL;DR: In this paper, the authors investigate how the non-analytic solitary wave solutions of an integrable bi-Hamiltonian system arising in fluid mechanics, can be recovered as limits of classical solitary wave solution forming analytic homoclinic orbits for the reduced dynamical system.