The sine-Gordon, Klein-Gordon, and Korteweg-de Vries equations (Q803764)

Three well-known equations of physics, i.e., the sine-Gordon, Klein- Gordon and Korteweg-de Vries equations are treated using decomposition. The solution is found as an n-term approximation \(\phi_ n=\sum^{n- 1}_{i=0}u_ i\) that converges to u as \(n\to \infty\). The aim is to obtain general solutions in terms of initial/boundary conditions when the physically correct conditions are known.