Abstract
A nonlinear transformation from the solution of linear KdV equation to the solution of Sharma-Tasso-Olver (STO) equation is derived out by using simplified homogeneous balance (SHB) method. According to the nonlinear transformation derived here, the exact explicit solution of initial (-boundary) value problem for STO equation can be constructed in terms of the solution of initial (-boundary) value problem for the linear KdV equation. The exact solution of the latter problem is obtained by using Fourier transformation.
Highlights
IntroductionFirst of all, we consider the initial value problem of STO equation as follows, ut + 3αu u x + 3α(uu x ) x + αu xxx = 0, t > 0, −∞ < x < ∞
Considering homogeneous balance between u xx and u3 (m + 2 = 3m, or m + 2 = 2m + 1, both equations imply m = 1), according to the simplified homogeneous balance (SHB) method [14,15,16,17], we suppose that the solution of Equation (1) is of the form, u( x, t) = A
In this paper, solving the initial (-boundary) value problem of STO equation has been changed into solving the initial (-boundary) value problem of the linear KdV equation based on the nonlinear transformation which has been derived by using SHB method for STO equation
Summary
First of all, we consider the initial value problem of STO equation as follows, ut + 3αu u x + 3α(uu x ) x + αu xxx = 0, t > 0, −∞ < x < ∞. We consider the initial-boundary value problem of STO equation with nonlinear boundary condition as follows, creativecommons.org/licenses/by/. We will find a function u( x, t) such that u = u( x, t) satisfies STO Equation (5) in the domain 0 < x < ∞, t > 0, and when t goes to zero, u( x, t) approaches to f ( x ), x ≥ 0 and when x goes to zero, the boundary condition in (6) is satisfied.
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
