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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 16
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 6, December 2009
  4. On Periodic solutions for a reduction of Benney chain
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 6, December 2009
Stationary solutions for the non-linear Hartree equation with a slowly varying potential
A remark on the existence and multiplicity result for a nonlinear elliptic problem involving the p-Laplacian
On Periodic solutions for a reduction of Benney chain
Sign-changing solutions and multiplicity results for elliptic problems via lower and upper solutions
Long-time behavior of solutions to Hamilton–Jacobi equations with quadratic gradient term
Periodic solutions for a class of non-autonomous differential delay equations
Discontinuous superlinear elliptic equations of divergence form
Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 5, October 2009
Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 4, August 2009
Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 3, July 2009
Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 2, April 2009
Nonlinear Differential Equations and Applications NoDEA : Volume 16, Issue 1, February 2009
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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On Periodic solutions for a reduction of Benney chain

Content Provider SpringerLink
Author Bialy, Misha
Copyright Year 2009
Abstract We study periodic solutions for a quasi-linear system, which naturally arises in search of integrable Hamiltonian systems of the form H = p 2/2 + u(q, t). Our main result classifies completely periodic solutions for such a 3 by 3 system. We prove that the only periodic solutions have the form of traveling waves so, in particular, the potential u is a function of a linear combination of t and q. This result implies that the there are no nontrivial cases of the existence of a fourth power integral of motion for H: if it exists, then it is equal necessarily to the square of a quadratic integral. Our main observation for the quasi-linear system is the genuine non-linearity of the maximal and minimal eigenvalues in the sense of Lax. We use this observation in the hyperbolic region, while the “elliptic” region is treated using the maximum principle.
Ending Page 743
Page Count 13
Starting Page 731
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 6
Volume Number 16
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2009-06-10
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Conservation laws Genuine nonlinearity Analysis Completely integrable systems and methods of integration Riemann invariants Benney chain Shocks and singularities Rich systems
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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