Analytical Solutions of the Fractional Complex Ginzburg-Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities

<div>The graphical simulation representation of <svg height="15.4254pt" id="M282" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.5914 51.7723 15.4254" width="51.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M715 650H476L470 622C550 619 562 610 562 570C562 536 553 481 535 384L523 321C485 121 408 37 283 37C178 37 99 109 134 297L178 532C193 612 199 616 278 622L284 650H29L23 622C105 616 109 609 94 532L48 291C23 160 51 83 98 40C143 -1 202 -16 260 -16C321 -16 387 3 439 49C509 111 542 204 563 312L577 384C595 479 608 533 619 569C629 603 637 620 709 622L715 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.873,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g 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style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g></svg> and for parameters <span class="nowrap"><svg height="12.5794pt" id="M284" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 271.92 12.5794" width="271.92pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 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Advances in Mathematical Physics

fig10

Figure 10

Figure 10: Analytical Solutions of the Fractional Complex Ginzburg-Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities 

Figure 10 | Analytical Solutions of the Fractional Complex Ginzburg-Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities 