Linear superposition of nonlinear waves

Linear superposition in nonlinear equations.

Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of so...

Linear Superposition in Nonlinear Wave Dynamics

We study nonlinear dispersive wave systems described by hyperbolic PDE’s in Rd and difference equations on the lattice Zd. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi–Pas...

Linear and nonlinear waves

The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acou...

Dynamic Analysis of Linear Structural Systems with Nonlinear Vibrating Isolators Using Mode Superposition Method

Dynamic Analysis of Linear Structural Systems with Nonlinear Vibrating Isolators Using Mode Superposition Method