Exact solutions of some fifth-order nonlinear equations. (English) Zbl 0954.35143

Summary: To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function \(U\) to be expressed as linear independent functions. The new soliton and periodic solutions of some fifth-order nonlinear partial differential equations \[ U_t+\alpha U^2U_x-\beta U_x U_{xx}-\gamma UU_{xxx}+ sU_{xxxxx}= 0 \] are obtained.


35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35C05 Solutions to PDEs in closed form
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