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The extended $$F$$-expansion method and its application for a class of nonlinear evolution equations. (English) Zbl 1138.35385
Summary: By means of a simple transformation technique, we have shown that the higher-order nonlinear Schrödinger equation in nonlinear optical fibers, a new Hamiltonian amplitude equation, generalized Hirota-Satsuma coupled system and generalized ZK-BBM equation can be reduced to an elliptic-like equation. Then, the extended $$F$$-expansion method is used to obtain a series of solutions including the single and the combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear evolution equations.

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 35Q55 NLS equations (nonlinear Schrödinger equations) 35C05 Solutions to PDEs in closed form 35A20 Analyticity in context of PDEs
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