Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation

Abstract

We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.

arXiv comment13 pages, 3 figures

References in corpus (1)

• On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour

Cited by in corpus (9)

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• Pole-free solutions of the first Painlevé hierarchy and non-generic critical behavior for the KdV equation
• "Quantization" of higher hamiltonian analogues of the Painleve I and Painleve II equations with two degrees of freedom
• Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation
• On the tritronquée solutions of P${}_I^2$
• The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systems
• Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type