Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Biến đổi Darboux, giải pháp soliton của phương trình Korteweg–de Vries phi địa phương với hệ số biến thiên
Tóm tắt
Trong bài báo này, phương trình Korteweg–de Vries phi địa phương đã được mở rộng thành dạng hệ số biến thiên dựa trên hệ thống AKNS. Biến đổi Darboux của phương trình Korteweg–de Vries phi địa phương với hệ số biến thiên được xây dựng. Một số nghiệm chính xác được thu được dựa trên biến đổi Darboux sử dụng nghiệm hạt giống bằng không và nghiệm hạt giống khác không, bao gồm nghiệm soliton đơn, nghiệm kink, nghiệm sóng thở và nghiệm sóng rogue. Kết quả cho thấy chúng tôi có thể thu được một số nghiệm tổng quát hơn so với dạng hệ số không đổi của nó.
Từ khóa
#phương trình Korteweg–de Vries #biến đổi Darboux #nghiệm soliton #hệ số biến thiên #sóng rogueTài liệu tham khảo
Ablowitz MJ, Musslimani ZH (2013) Integrable nonlocal nonlinear Schrödinger equation. Phys Rev Lett 110:064105
Ablowitz MJ, Musslimani ZH (2016) Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation. Nonlinearity 29:915
Ablowitz MJ, Kaup DJ, Newell AC, Segur H (1974) The inverse scattering transform-Fourier analysis for nonlinear problems. Stud Appl Math 53:249
Anderson IM, Fels ME (2016) Bäcklund transformations for Darboux integrable differential systems: examples and applications. J Geom Phys 102:1–31
Antonelli P, Marcati P, Zheng H (2019) Stability for the quadratic derivative nonlinear Schrödinger equation and applications to the Korteweg–Kirchhoff type Euler equations for quantum hydrodynamics. Nonlinear Anal 186:209–218
Bashan A (2020) An effective approximation to the dispersive soliton solutions of the coupled KdV equation via combination of two efficient methods. Comput Appl Math 39:80
Congy T, Ei GA, Hoefer MA, Shearer M (2019) Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Stud Appl Math 142:241–268
Coz SL, Wang Z (2021) Stability of the multi-solitons of the modified Korteweg–de Vries equation. Nonlinearity 34:7109
Ding CC, Gao YT, Deng GF, Wang D (2020) Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled nonautonomous nonlinear Schrödinger system in an inhomogeneous plasma. Chaos Solitons Fractals 133:109580
Ji JL, Zhu ZN (2017) On a nonlocal modified Korteweg–de Vries equation: integrability, Darboux transformation and soliton solutions. Commun Nonlinear Sci Numer Simul 42:699–708
Lan ZZ (2020) Rogue wave solutions for a higher-order nonlinear Schrödinger equation in an optical fiber. Appl Math Lett 107:106382
Li BQ, Ma YL (2020) Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrodinger equation. Appl Math Comput 386:125469
Li M, Zhang Y, Ye R, Lou Y (2021) Exact solutions of the nonlocal Gerdjikov–Ivanov equation. Commun Theor Phys 73:105005
Liu W, Zheng XX, Li XL (2018) Bright and dark soliton solutions to the partial reverse space-time nonlocal Mel’nikov equation. Nonlinear Dyn 94:2177–2189
Liu YQ, Wen XY, Wang DS (2019) The N-soliton solution and localized wave interaction solutions of the (2 + 1)-dimensional generalized Hirota–Satsuma–Ito equation. Comput Math Appl 77:947–966
Liu FY, Gao YT, Yu X, Hu L, Wu XH (2021) Hybrid solutions for the (2+1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics. Chaos Soliton Fractals 152:111355
Namjoo M, Zibaei S (2018) Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes. Comput Appl Math 37:1395–1411
Nandy S, Barthakur A (2019) Pairwise three soliton interactions, soliton logic gates in coupled nonlinear Schrödinger equation with variable coefficients. Commun Nonlinear Sci Numer Simul 69:370–385
Osman MS (2018) On multi-soliton solutions for the (2 + 1)-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide. Comput Math Appl 75:1–6
Ren RC, Zhang SL (2020) Invariant analysis, conservation laws, and some exact solutions for (2 + 1)-dimension fractional long-wave dispersive system. Comput Appl Math 39:249
Song JY, Hao HQ (2019) Darboux transformation and explicit solutions for the (2 + 1)-dimensional nonlocal nonlinear Schrödinger–Maxwell–Bloch system. Appl Math Lett 96:166–171
Wang XF, Cheng H (2021) Solitary wave solution and a linear mass-conservative difference scheme for the generalized Korteweg–de Vries–Kawahara equation. Comput Appl Math 40:273
Wang X, Wang L (2018) Darboux transformation and nonautonomous solitons for a modified Kadomtsev–Petviashvili equation with variable coefficients. Comput Math Appl 75:4201–4213
Wang H, Tian SF, Zhang TT, Chen Y, Fang Y (2019) General lump solutions, lumpoff solutions, and rogue wave solutions with predictability for the (2 + 1)-dimensional Korteweg–de Vries equation. Comput Appl Math 38:164
Wazwaz AM (2013) On the nonlocal Boussinesq equation: multiple-soliton solutions. Appl Math Lett 26:1094–1098
Xin XP, Liu YT, Xia YR, Liu HZ (2021) Integrability, Darboux transformation and exact solutions for nonlocal couplings of AKNS equations. Appl Math Lett 119:107209
Zhang XE, Chen Y, Zhang Y (2017) Breather, lump and X soliton solutions to nonlocal KP equation. Comput Math Appl 74:2341–2347
Zhang QY, Zhang Y, Ye R (2019) Exact solutions of nonlocal Fokas–Lenells equation. Appl Math Lett 98:336–343
Zhou ZX (2018) Darboux transformations and global explicit solutions for nonlocal Davey–Stewartson I equation. Study Appl Math 141:186–204