Soliton Rectangular Pulses and Bound States in a Dissipative System Modeled by the Variable-Coefficients Complex Cubic-Quintic Ginzburg–Landau Equation

Abstract

The complex cubic-quintic Ginzburg-Landau equation (CQGLE) is a universal model for describing a dissipative system, especially fiber laser. The analytic one-soliton solution of the variable-coefficients CQGLE is calculated by a modified Hirota method. Then, phenomena of soliton pulses splitting and stable bound states of two solitons are investigated. Moreover, rectangular dissipative soliton pulses of the variable-coefficients CQGLE are realized and controlled effectively in the theoretical research for the first time, which breaks through energy limitation of soliton pulses and is expected to provide theoretical basis for preparation of high-energy soliton pulses in fiber lasers.

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.…”

Evolution of periodic wave and dromion-like structure solutions in the variable-coefficients coupled high-order complex Ginzburg-Landau system

“…The propagation characteristics of the optical soliton in an ideal optical fiber are generally represented by the nonlinear schrödinger equation (NLSE) [19][20][21][22][23][24]. But the optical fiber in an actual optical communication system is accompanied by gain or loss, and at this time, the system needs to be modeled by the complex Ginzburg-Landau equation (CGLE) [25][26][27][28][29]. At the same time, in the modern optical communication system, to optimize information transmission efficiency and reduce cost, the Wavelength Division Multiplexing (WDM) technology has been proposed [30][31][32].…”