Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion

Nonexistence of travelling wave solution of the Korteweg-de Vries Benjamin Bona Mahony equation

“…We consider some initial data (at � = ��) for a traveling wave. In this case, we note that the nonexistence of a solution to equation 5depends on the conditions (8).…”

“…In [8], traveling-wave solutions �(�, �) � = ��(��� ���) are sought for the equation 3which describes wave the processes in semiconductors with strong spatial dispersion. In [8][9][10][11][12] the authors obtained sufficient conditions for the finite time blow-up of solutions of time and space initial problems for the Korteweg-de Vries and Benjamin-Bona-Mahony type equations.…”

1-Soliton solution and conservation laws for nonlinear wave equation in semiconductors

“…The dimensionless form of the nonlinear wave equation that is going to be studied in this paper is given by Al'shin et al [1] q t þ aqq x þ bq xxx þ cq xxt ¼ 0; system consisting of the stationary field equations, continuity equation and constitutive equation. Finally, the Columb potential is introduced that leads to the formulation of (1) [1].…”

“…Finally, the Columb potential is introduced that leads to the formulation of (1) [1]. It needs to be noted that (1) is also known as the improved Korteweg-de Vries (KdV) equation that appears in the study of shallow water waves, in Fluid Dynamics [14].…”

“…The study of nonlinear waves is being carried out in various areas of Physics and Engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. These include Nonlinear Optics, Fluid Dynamics, Biophysics, Nuclear Physics, Plasma Physics and many more.…”