Soliton interaction control through dispersion and nonlinear effects for the fifth-order nonlinear Schrödinger equation

Breathers, Rogue waves, Chirp-free solitons and M-shape solitons with carbon nanotube as saturable absorbe in the ring-cavity fiber system

“…We have attained multiwave solution by using three waves assumption on f in (13). The MS profiles for Υ11 (55) are displayed via b0 = 1.5, c2 = 2, b2 = −5, s1 = −3, s3 = 4, k1 = 4, k2 = 2.5, a4 = 3.5, a2 = 3, a6 = 2.5, n1 = 6, n3 = 2, c1 = 3 in Fig. 8.…”

Propagation characteristics of bright and mixed solitons based on the variable coefficient (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation

“…孤子这一概念在如非线性光学、原子物 理、凝聚态物理等诸多领域得到关注和应 用 [1][2][3][4] 。由于通常在介质中传播的光波或 脉冲其电磁包络非单色性，各部分会因为 传播速度不同而导致包络展宽。如在空间维 度，光波因为衍射效应使光束半径增大，在 时间维度则由于群速度色散致使脉冲展宽。 因而，在特殊条件下利用传播介质的非线性 效应或直接使用光纤放大器实现衰减补偿， 使非线性效应与衍射效应和色散效应达到平 衡，可以弥补线性传输过程中光波或脉冲的 发散 [5][6][7][8] 。这样的孤子具有稳定的、局域的、 类粒子的特性，被叫做光孤子。 根据光孤子所在的色散区域不同，光孤 子可分为明孤子和暗孤子。光孤子具有一系 列重要的应用价值 [9][10][11][12][13][14][15][16][17][18][19] ，例如将光孤子当作 比特信息应用于超快光学数字逻辑系统；还 可以研究超快光与物质之间的非线性相互作 用；应用于远程通信系统时，其中孤子的传 播可以用三次-五次复金兹堡-朗道(CGL)方 程来建模 [20][21][22] 。 三次-五次 CGL 方程是对被动锁模激光 器中区域动力学的一个持续估计 [23] CGL 方程 [24] ：…”

Characteristics of dynamic waves in incompressible fluid regarding nonlinear Boiti-Leon-Manna-Pempinelli model

“…Jacobi elliptic function scheme [7,8], extended simplest equation technique [9][10][11], Fexpansion method [12,13], trial equation scheme [14,15], various rational (𝐺 ′ /𝐺)-expansion tools [16][17][18], exp-function approach [19,20], improved tanh approach [21], Darboux transformation approach [22], different Hirota schemes [23][24][25][26][27], Kudryashov technique [28] etc. This present study is conducted by implementing two competent techniques such as improved tanh and improved auxiliary equation.…”