Abstract
We have used the modified variational iteration method (MVIM) to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers‐Fisher equation, the Kuramoto‐Sivashinsky equation, the coupled Schrodinger‐KdV equations, and the long‐short wave resonance equations together with initial conditions. The results of these problems reveal that the modified variational iteration method is very powerful, effective, convenient, and quite accurate to systems of nonlinear equations. It is predicted that this method can be found widely applicable in engineering and physics.
Highlights
Nonlinear partial differential equations are known to describe a wide variety of phenomena in physics, where applications extend over magnetofluid dynamics, water surface gravity waves, electromagnetic radiation reactions, and ion acoustic waves in plasma, and in biology, chemistry, and several other fields
We find the solutions u x, t and v x, t satisfying the nonlinear coupled Schrodinger-KdV equations 1.3 with the following initial conditions 41 : u x, 0 −cα 2αk tanh ikx, v x, 0 −2k2sech[2] ikx, 5.13 where k, α, and c are arbitrary constants and α 2k2 c/2
We find the solutions u x, t and v x, t satisfying the nonlinear long–short wave resonance equations 1.4 with the following initial conditions 42 : v0 u x, 0 k β
Summary
Nonlinear partial differential equations are known to describe a wide variety of phenomena in physics, where applications extend over magnetofluid dynamics, water surface gravity waves, electromagnetic radiation reactions, and ion acoustic waves in plasma, and in biology, chemistry, and several other fields. It is one of the important tasks in the study of the nonlinear partial differential equations to seek exact and explicit solutions. The main objective of the present paper is to use the modified variational iteration method MVIM for constructing the traveling wave solutions of the following nonlinear partial differential equations in mathematical physics:. Equation 1.3 describe various processes in dusty plasma such as Langmuri, dust-acoustic wave and electromagnetic waves, while in 1.4 u is the envelope of the short wave and is a complex function, and v is the amplitude of the long wave which is a real function
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
