Asymptotics of oscillatory Riemann–Hilbert problems
Copyright policy )Asymptotics of oscillatory Riemann–Hilbert problems
A classical method of stationary phase for oscillatory integrals is generalized to oscillatory Riemann–Hilbert problems of the kind arising in the theory of integrable nonlinear equations. The proposed approach is developed for the phase with N first-order stationary points, and the final formulas can immediately be applied to the problem of long-time behavior of the solutions of equations such as the NLS, KdV, mKdV sine-Gordon, and others.
- St Petersburg University Russian Federation
oscillatory Riemann-Hilbert problems, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, long-time behavior of the solutions, KdV equations (Korteweg-de Vries equations), Riemann-Hilbert problems in context of PDEs, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
oscillatory Riemann-Hilbert problems, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, long-time behavior of the solutions, KdV equations (Korteweg-de Vries equations), Riemann-Hilbert problems in context of PDEs, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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