Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations
نویسندگان
چکیده
منابع مشابه
Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations
We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the AKNS and the KN classes, based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair. Along with the well known equations we discover a novel integrable hierarchy of higher order nonholonomic deformations for the AKNS family, e.g. for the KdV, the m...
متن کاملNonlinearizing linear equations to integrable systems including new hierarchies of nonholonomic deformations
We propose a scheme for nonlinearizing linear equations to generate integrable systems of both the AKNS and the KN classes, based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair. Along with the well known equations we discover a novel integrable hierarchy of higher order nonholonomic deformations for the AKNS family, e.g. the KdV, the mKdV, the NLS a...
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15 صفحه اولReciprocal Transformations and Deformations of Integrable Hierarchies
j=s aiD i x and [K]i = ai, and ǫ is an arbitrary constant. The compatibility conditions for (2) and (3) read Ltq = [P≥1(L ) + ǫ[L]0Dx, L], q = 1, 2, . . . . (4) Note that the hierarchy (4) with ǫ = 0 was discovered by Kupershmidt [2]. The goal of the present work is to show that, under a suitable change of dependent and independent variables x, ti, and uk, the “deformed” hierarchy (4) can be tr...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2009
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3204081