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The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown that the solution of the two-component nonlinear wave oscillates with the sum and difference of frequencies and wave numbers.
Using the generalized perturbation reduction method the Hirota equation is transformed to the coupled nonlinear Schrodinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The component
In this work, we employ the generalized perturbation reduction method to find the two-component vector breather solution of the cubic Boussinesq equation $U_{tt} - C U_{zz} - D U_{zzzz}+G (U^{3})_{zz}=0$. Explicit analytical expressions for the shape
The generalized perturbative reduction method is used to find the two-component vector breather solution of the nonlinear Klein-Gordon equation. It is shown that the nonlinear pulse oscillates with the sum and difference of frequencies and wave numbe
Using the generalized perturbation reduction method the scalar nonlinear Schrodinger equation is transformed to the coupled nonlinear Schrodinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is o
We show that the nonlinear stage of modulational instability induced by parametric driving in the {em defocusing} nonlinear Schrodinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong drivi