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

• Autorzy: Yuan Feng , Zhu Xiaoming , Wang Yulei

Identyfikatory

DOI

10.34768/amcs-2020-0026

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Korteweg–de Vries equation; Darboux transformation; deformed soliton solution

PL

równanie Kortewega-de Vries; transformacja Darboux; soliton zdeformowany

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 2
• Strony: 337--350
• Opis fizyczny: Bibliogr. 43 poz., wykr.

Twórcy

autor

Yuan Feng

• School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, PR China

autor

Zhu Xiaoming

• School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, PR China

autor

Wang Yulei

• Department of Engineering and Applied Physics, University of Science and Technology of China, Hefei, Anhui 230026, PR China

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).