Methods and Applications of Analysis, Volume 4International Press, 1997 - Mathematical analysis |
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analysis apply approximate solutions arbitrary asymptotic expansion B₁ behavior bounded C₁ classical coefficients computed conservation laws constant convergence corresponding defined denote derivative discrete entropy estimate exists exponential finite formula gamma function given Hamiltonian Hence hyperbolic I-curve incomplete gamma function initial data integral interaction interpolation invariant KdV equation Kruskal Lemma linear manifold mapping Math Mathematics Subject Classification Miura modulation N₁ NLS equation nonclassical method nonlinear obtain ordinary differential equations orthogonal polynomials oscillatory Painlevé equations parameter partial differential equations perturbation Phys points problem Proof q-exponential r₁ recurrence relation reduced flow respectively result Riemann S₁ satisfies Section sequence shock wave soliton stationary sufficiently small symmetry reductions t₁ Theorem transformation u₁ v₁ values variables vector Zapprox zero