<abstract xmlns="http://www.w3.org/1999/xhtml">Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the determinant form of the <italic>n</italic>-fold Darboux transformation for these (2+1)-dimensional cmKdV equations, we obtain general order-<italic>n</italic> deformed soliton solutions using zero seeds. With no loss of generality, we focus on order-1 and order-2 deformed solitons. Three types of order-1 deformed solitons, namely, the polynomial type, the trigonometric type, and the hyperbolic type, are derived. Meanwhile, their dynamical behaviors, including amplitude, velocity, direction, periodicity, and symmetry, are also investigated in detail. In particular, the formulas of |<italic>q</italic>[1]| and trajectories are provided analytically, which are involved by an arbitrary smooth function <italic>f</italic>(<italic>y</italic> + 4<italic>λ</italic>2<italic>t</italic>). For order-2 cases, we obtain the general analytical expressions of deformed solitons. Two typical solitons, possessing different properties in temporal symmetry, are discussed.</abstract>

Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the determinant form of the n-fold Darboux transformation for these (2+1)-dimensional cmKdV equations, we obtain general order-n deformed soliton solutions using zero seeds. With no loss of generality, we focus on order-1 and order-2 deformed solitons. Three types of order-1 deformed solitons, namely, the polynomial type, the trigonometric type, and the hyperbolic type, are derived. Meanwhile, their dynamical behaviors, including amplitude, velocity, direction, periodicity, and symmetry, are also investigated in detail. In particular, the formulas of |q[1]| and trajectories are provided analytically, which are involved by an arbitrary smooth function f(y + 4λ2t). For order-2 cases, we obtain the general analytical expressions of deformed solitons. Two typical solitons, possessing different properties in temporal symmetry, are discussed.

Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations

University of Science and Technology of China

Department of Engineering and Applied Physics

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the...

Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations

Published Online: Jul 04, 2020

Page range: 337 - 350

Received: Nov 15, 2019

Accepted: Jan 30, 2020

DOI: https://doi.org/10.34768/amcs-2020-0026

Keywords
(2+1)-dimensional complex modified Korteweg–de Vries equation, Darboux transformation, deformed soliton solution

© 2020 Feng Yuan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations

Published Online: Jul 04, 2020

Page range: 337 - 350

Received: Nov 15, 2019

Accepted: Jan 30, 2020

DOI: https://doi.org/10.34768/amcs-2020-0026

Keywords(2+1)-dimensional complex modified Korteweg–de Vries equation, Darboux transformation, deformed soliton solution

© 2020 Feng Yuan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
(2+1)-dimensional complex modified Korteweg–de Vries equation, Darboux transformation, deformed soliton solution