Abstract A generalization of the addition relation for the Riemann theta functions and its limiting version for exponential functions appearing in soliton type equations are reported. The presented form seems to be particularly useful when processes in N + 1, (N > 1) space-time are analyzed. The commonly applied bilinear and trilinear approaches, restricted to the pure soliton processes, repres...

In this paper, we study a new negative-order KdV-CBS equation in (3+1) dimensions which is combination of the Korteweg-de Vries (KdV) and Calogero–Bogoyavlenskii–Schiff (CBS) equation. Firstly, determine Lie point symmetries conservation laws by using multiplier method. The will be used to obtain triple reduction second order ordinary differential (ODE), lead line travelling waves soliton solut...

The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications plasma physics soliton theory, where it forecasts the wave propagation profiles. In order to obtain analytically exact solitons, model under consideration a nonlinear partial differential that turned into an ordinary by using next traveling transformation. new exte...

In this research, analytical and semi-analytical soliton solutions for the nonlinear fractional (2 + 1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation (FCBSE) in non-local form are obtained using recent computational numerical methods. The FCBSE is a significant model investigating various phenomena, such as internal ocean waves, tsunamis, river tidal magneto-sound waves plasma....