Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation

Abstract

Starting from a general sixth-order nonlinear wave equation, we present its multiple kink solutions, which are related to the famous Hirota form. We also investigate the restrictions on the coefficients of this wave equation for possessing multiple kink structures. By introducing the velocity resonance mechanism to the multiple kink solutions, we obtain the soliton molecule solution and the breather-soliton molecule solution of the sixth-order nonlinear wave equation with particular coefficients. The three-dimensional image and the density map of these soliton molecule solutions with certain choices of the involved free parameters are well exhibited. After matching the parametric restrictions of the sixth-order nonlinear wave equation for having three-kink solution with the coefficients of the integrable bidirectional Sawada–Kotera–Caudrey–Dodd–Gibbons (SKCDG) equation, the breather-soliton molecule solution for the bidirectional SKCDG equation is also illustrated.

Vortex Quantum Droplets under Competing Nonlinearities

“…(a) (b) The effective 2D LHY-corrected GPE (11) gives rise to stable VQD solutions. [56] 11) remain stable up to 𝑆 = 5 when 𝑁 exceeds a threshold value, which scales as 𝑁 th ∼ 𝑆 4 .…”

“…Research of self-localized states in nonlinear physics involves the use of mathematical modeling, numerical simulations, and experimental techniques to predict and demonstrate spatially confined stable structures, such as solitons and breathers. [1][2][3][4][5][6][7] These phenomena find diverse applications in optical communications, [8,9] condensed-matter physics, [10][11][12][13] and quantum technologies, [14][15][16][17] contributing to advancements in understanding nonlinear behavior of many physical systems. As topologically organized self-localized states, vortices with winding number 𝑆 are rotationally symmetric structures with encircling phase distributions representing the 2𝜋𝑆 net phase change.…”

All-Optical Switches for Optical Soliton Interactions in a Birefringent Fiber

“…Optical solitons have the characteristics of low bit error rate, long transmission distance, and large capacity in fiber optic communication, and can be used for the transmission of a large amount of information, which has always been favored by scientists. [1][2][3][4][5] In recent years, scientists have been trying to build all-optical networks, and an important aspect is the need to manufacture all-optical switches. Using the interaction of optical solitons to manufacture alloptical switches is one of the very feasible solutions.…”

Multi-Pseudo Peakons in the b-Family Fifth-Order Camassa–Holm Model

“…In the field of integrable system and soliton, it is of importance to investigate new integrable models such as higher order systems [17][18][19][20] and solitary waves interaction. [21][22][23][24][25][26] In recent years, some kinds of higherorder Camassa-Holm equation and their peakon solutions have attracted much attention, [27][28][29][30][31][32][33][34] which are of great theoretical significance in the CH type models and widely enrich the physical phenomena generated by the CH equation.…”