Wave propagation behavior within 1D granular chain has been a much-studied topic in the
past decades due to its novel physical wave phenomena. The initial motivation of the …

This paper develops an analytic study on the existence and properties of solitary waves on
1D chains of lumped masses and nonlinear springs, which exhibit a mechanical response …

All nonlinear dispersive wave equations in the general class $ m_t+ f (u, u_x) m+(g (u, u_x)
m) _x= 0$ are known to possess multi-peakon weak solutions. A classification is presented …

In this paper we have considered the (2+ 1)(2+ 1) filtration-absorption equation that models
the flow of impure water in a water-absorbing fissured porous medium. We have applied the …

For the generalized p-power Korteweg–de Vries equation, all non-periodic travelling wave
solutions with non-zero boundary conditions are explicitly classified for all integer powers …

Properties of solitary waves in precompressed Hertzian chains of particles are studied in the
long-wavelength limit using a well-known continuum model. Several main results are …

For a Hertz chain model, by using the methodology of dynamical systems and singular
traveling wave theory developed by Li and Chen [9] to its traveling wave system defined on …

We investigated the head-on collision between two envelope solitary waves. Head-on
collisions between two envelope solitary waves are first discussed in one-dimension (1D) …

Properties of solitary waves in weakly pre-compressed Hertzian chains are studied in the
long wavelength regime using a well-known continuum model. Several main results are …

In presenting this thesis, we try to find all non-periodic travelling waves of the generalized
Korteweg-de Vries (gKdV) equation u_t+\alpha u^ p u_x+\beta u_ {xxx}= 0 using an energy …