On the integrability of nonlinear partial differential equations

Details On the integrability of nonlinear partial differential equations On the integrability of nonlinear partial differential equations

1998-07-22

arxiv.org/abs/solv-int/9807007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages Latex

Scientific paper

We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV equation to other NPDEs. The method is based upon a linearization principle which can be applied on nonlinearities which have a polynomial form. We illustrate the potential of the method by finding solutions of the (coupled) nonlinear Schr\"{o}dinger equation and the Manakov equation which play an important role in optical fiber communication. Finally, it is shown that the method can also be generalized to higher-dimensions.

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