Consequences of scaling in nonlinear partial differential equations
作者： Nino R. Pereira
DOI: 10.1063/1.523007
关键词: Mathematics 、 Inverse scattering transform 、 Korteweg–de Vries equation 、 Partial differential equation 、 Hyperbolic partial differential equation 、 Separable partial differential equation 、 Mathematical analysis 、 Inverse scattering problem 、 First-order partial differential equation 、 Differential equation 、 Mathematical physics 、 Statistical and Nonlinear Physics
摘要: Scaling of the form x=ax′, t=aht′, q=amQ a nonlinear partial differential equation for q is connected with auxiliary functions in an inverse scattering method (AKNS scheme). Solvability by this scheme treated. It shown that only equations m=2 are solvable using conjunction Schrodinger eigenvalue equation. The criterion restricts terms these equations. terms, powers and its derivatives, can be found inspection. A separate problem, decay single soliton Korteweg–de Vries damping, solved scaling properties.
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