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The first-integral method applied to the Eckhaus equation. (English) Zbl 1242.35078
Summary: The first-integral method is a direct algebraic method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. In this work, we apply the first-integral method to study the exact solutions of the Eckhaus equation.

MSC:
35C05 Solutions to PDEs in closed form
35A25 Other special methods applied to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
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