Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
Copyright policy )Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of 2nd order systems with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.
60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus several minor changes, to appear in J.Phys.A
- Brock University Canada
- Kwansei Gakuin University Japan
lists of second-order systems, Soliton equations, Software, source code, etc. for problems pertaining to partial differential equations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Lax representation, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), weighting of variables, FOS: Physical sciences, classification of integrable systems, Mathematical Physics (math-ph), KdV equations (Korteweg-de Vries equations), higher symmetries, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
lists of second-order systems, Soliton equations, Software, source code, etc. for problems pertaining to partial differential equations, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Lax representation, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), weighting of variables, FOS: Physical sciences, classification of integrable systems, Mathematical Physics (math-ph), KdV equations (Korteweg-de Vries equations), higher symmetries, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
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