The Nonlinear Schrödinger Equation Derived From the Fifth-Order Korteweg–de Vries Equation Using Multiple Scales Method

The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems. Although the origin of nonlinear evolution equations dates back to ancient times, significant developments have been made in these equations up to the present day. The main reason for this situation is that NLEE involve the problem of nonlinear wave propagation. Therefore, many different and effective techniques have been developed regarding nonlinear evolution equations and solution methods. Studies conducted in recent years show that evolution equations are becoming increasingly important in applied mathematics. This study is about the multiple scales methods, known as the perturbation method, for NLEE. In this report, the multiple scales method was applied for the analysis of (1 + 1) dimensional fifth-order nonlinear Korteweg–de Vries (KdV) equation, and nonlinear Schrödinger (NLS) type equations were obtained.