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2015•Journal of Nonlinear Mathematical PhysicsOpen access

On generalized Lax equation of the Lax triple of KP Hierarchy

Xiaoli Wang, Lu Yu, Yanxin Yang, Min-Ru Chen

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Abstract

In terms of the operator Nambu 3-bracket and the Lax pair (L, B n ) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, B n , B m ).The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized Lax equation with the different Lax triples (L, B n , B m ).Furthermore we derive some no integrable evolution equations and present their single soliton solutions.

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In terms of the operator Nambu 3-bracket and the Lax pair (L, B n ) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, B n , B m ).The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized Lax equation with the different Lax triples (L, B n , B m ).Furthermore we derive some no integrable evolution equations and present their single soliton solutions.

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Available abstract

In terms of the operator Nambu 3-bracket and the Lax pair (L, B n ) of the KP hierarchy, we propose the generalized Lax equation with respect to the Lax triple (L, B n , B m ).The intriguing results are that we derive the KP equation and another integrable equation in the KP hierarchy from the generalized Lax equation with the different Lax triples (L, B n , B m ).Furthermore we derive some no integrable evolution equations and present their single soliton solutions.

Key concepts: Lax pair, Mathematics, Hierarchy, Pure mathematics, Kadomtsev–Petviashvili equation, Algebra over a field, Mathematical analysis, Mathematical physics

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