Complexiton Solutions of a Special Coupled mKdV System

Abstract

For a special coupled mKdV system, which can be derived from a two-layer fluid model, Hirota's bilinear direct method is used to construct and yield the complexiton solutions. The detailed physical properties of complexitons are further illustrated graphically.

Bright solitons and multiple soliton solutions for coupled modified KdV equations with time-dependent coefficients

“…As stated before, this model is derived from a two-layer fluid model, which is used to study the interaction between the atmosphere and oceanic phenomena. The derivation of ( 6) was achieved by using the multiple-scale approach with the reductive perturbation method [5].…”

“…Various methods [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have been used to investigate the coupled nonlinear KdV and mKdV equations. Examples of the methods that have been used are the Hirota bilinear method, the Bäcklund transformation method, Darboux transformation, the Pfaffian technique, the inverse scattering method, Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method (sub-ODE for short) [6], the coupled amplitude-phase formulation [9], the sine-cosine method [10], the sech-tanh method [11], the mapping and the deformation approach, and many other methods.…”

“…Examples of the methods that have been used are the Hirota bilinear method, the Bäcklund transformation method, Darboux transformation, the Pfaffian technique, the inverse scattering method, Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method (sub-ODE for short) [6], the coupled amplitude-phase formulation [9], the sine-cosine method [10], the sech-tanh method [11], the mapping and the deformation approach, and many other methods. Hirota's bilinear method [5][6][7][8][9][10][11] and Hereman's simplified form [19] are rather heuristic and significant. These approaches possess powerful features that make the determination of multiple soliton solutions [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] practical for a wide class of nonlinear evolution equations.…”