About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

DOI10.1063/1.4795132zbMath1298.37049arXiv1110.1626OpenAlexW2022279944MaRDI QIDQ5397783

A. V. Topovsky, V. G. Dubrovskij

Publication date: 24 February 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.1626

zbMATH Keywords

exact solutionsdressing methodsuperposition of solutionsVeselov-Novikov equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (1)

Two kinds of important bifurcation phenomena of nonlinear waves in a generalized Novikov-Veselov equation

Cites Work

• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• Construction of higher-dimensional nonlinear integrable systems and of their solutions
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• Bell's inequality without alternative settings
• Inverse scattering problem for the two-dimensional Schrödinger operator, the \({\bar\partial}\)-method and nonlinear equations
• New exact solutions with functional parameters of the Nizhnik-Veselov-Novikov equation with constant asymptotic values at infinity
• The construction of exact rational solutions with constant asymptotic values at infinity of two-dimensional NVN integrable nonlinear evolution equations via the $\overline{\partial}$-dressing method
• Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity
• The non-local delta problem and (2+1)-dimensional soliton equations
• On the Moutard transformation for integrable partial differential equations

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