Weak asymptotics method and the interaction of infinitely narrow \(\delta\)-solitons.

DOI10.1016/S0362-546X(03)00104-4zbMath1040.35092MaRDI QIDQ1399951

Vladimir G. Danilov, Georgii A. Omel'yanov

Publication date: 30 July 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

KdV-type equationweak asymptotics methodsmall dispersioninteraction of solitonsweak asymptotic solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Initial value problems for nonlinear higher-order PDEs (35G25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (13)

Collision of solitons in non-integrable versions of the Degasperis-Procesi model ⋮ Weak multi-phase asymptotics for nonintegrable equations ⋮ Soliton‐type asymptotics for non‐integrable equations: a survey ⋮ Propagation and interaction of solitons for nonintegrable equations ⋮ Irregular shock waves formation as continuation of analytic solutions ⋮ Interaction of solitons for sine-Gordon-type equations ⋮ Anomalous solutions to nonlinear hyperbolic equations ⋮ A triangle-based positive semi-discrete Lagrangian-Eulerian scheme via the weak asymptotic method for scalar equations and systems of hyperbolic conservation laws ⋮ Multi-soliton Collision for Essentially Nonintegrable Equations ⋮ Uniform in time description for weak solutions of the Hopf equation with nonconvex nonlinearity ⋮ Interaction of kinks for semilinear wave equations with a small parameter ⋮ Weak asymptotic methods for scalar equations and systems ⋮ Collision of Solitons for a Non-homogenous Version of the KdV Equation: Asymptotics and Numerical Simulation

Cites Work

• Dispersive blowup of solutions of generalized Korteweg-de Vries equations
• On the smoothing properties of solutions to the modified Korteweg-de Vries equation
• Generalized solutions describing singularity interaction
• The small dispersion limit of the korteweg-de vries equation. ii
• The small dispersion limit of the Korteweg-de Vries equation. I
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