Titlebook: Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics; Generalized Solitons John P. Boyd Book 1998 Springer Science+Business Med

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The Method of Multiple Scales and the ∈-Power Seriesdimensional reality is approximated by one-dimensional models such as the Korteweg-deVries equation. One might call this “reduction of dimension”. Second, it can be applied within the microworld of one-dimensional wave equations to generate further approximations, such as FKdV ∈-series in which the lowest order is the KdV solitary wave.

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Nonlinear Algebraic Equations the phase speed . is the eigenvalue and the shape of the wave .(.;.) is the eigenfunction. The theme of this chapter is: How to solve the discretized equivalent of such a nonlinear eigenproblem: a system of . nonlinear algebraic equations in . unknowns, depending continuously on an eigenparameter.

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初学者

Matched Asymptotic Expansions in the Complex Planeprevious chapter, the multiple scales series is a good approximation to the core of the nanopteron even though it diverges factorially. However, the ∈-power series gives no information about the radiation coefficient.

魅力

Stokes’ Expansion, Resonance & Polycnoidal Waves, infinitely long, and infinitesimally small in amplitude. Graduate students are initiated into the next level of illumination through the counter-idealization of the soliton: also steady but for phase propagation, but spatially localized instead of infinitely delocalized, intrinsically nonlinear instead of negligibly nonlinear.

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Nonlinear Algebraic Equations the phase speed . is the eigenvalue and the shape of the wave .(.;.) is the eigenfunction. The theme of this chapter is: How to solve the discretized equivalent of such a nonlinear eigenproblem: a system of . nonlinear algebraic equations in . unknowns, depending continuously on an eigenparameter.

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