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
p⩾ 1. These solutions are shown to consist of: bright solitary waves and static humps on a
non-zero background for odd p; dark solitary waves on a non-zero background and kink
(shock) waves for even p in the defocusing case; pairs of bright/dark solitary waves on a non-
zero background, and also bright and dark heavy-tail waves (with power decay) on a non …

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
analysis method. Since the power p in the gKdV equation is arbitrary, we consider positive
integer values for $ p $. We first check the method for two cases where p= 1 and p= 2 which
are known as the KdV and the mKdV equations, respectively. Then, we look at the general
case where p greater than or equal 3 is arbitrary. By applying the energy analysis method on …