Bifurcation and new traveling wave solutions for the 2D Ginzburg–Landau equation

Dynamical Behaviour of Conformable Time-Fractional Coupled Konno-Oono Equation in Magnetic Field

“…e integration of Eq. ( 16) requires appropriate domains of the constants C, a, ω, and h. e domains of these constants can be found by applying distinct methods such as a complete discriminant method [60] for the quartic polynomial −ψ 4 + 2Cψ 2 + 2a 2 ω 2 h and bifurcation analysis [39][40][41][42][43][44][45][46][47][48]. e bifurcation analysis is more significant because it gives the range of those parameters and specifies the kind of the solution before constructing them.…”

“…In this work, we study the existence and the type of some novel traveling wave solutions for (2) by the qualitative theory of planar dynamical system which has been applied successfully in various works such as [39][40][41][42][43][44][45][46][47][48] before constructing them through the kind of the orbits. For instance, the existence of periodic, homoclinic, and heteroclinic orbits imply to the existence of periodic, solitary, and kink (or antikink) wave solutions.…”

Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model

“…He's variational method, introduced in [85], is a successful method for finding approximated solitary wave solutions. We desire to find the bright soliton for equation (27) in the following formula:…”

“…Researchers are therefore motivated to present new methods and refine existing approaches. Various significant and powerful methods have been introduced such as Darboux transformation [14], Weierstrass elliptic functions methods [15,16], Bäcklund transformation [17], Lie group [18][19][20][21], Hirota's method [22,23], bifurcation method [24][25][26][27][28][29][30][31][32][33], and for distinct method, as shown in e.g., [34][35][36][37][38][39][40][41][42]. e analytical and numerical solutions for various types of nonlinear partial differential equations were investigated using traditional Lie symmetry approaches; for instance as shown in [43].…”

New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative

“…The Ginzburg-Landau (GL) equation [1][2][3][4][5][6][7] is one of the most important partial differential equations in the field of mathematics and physics, which was introduced into the study of superconductivity phenomenology theory in the 20th century by Ginzburg and Landau. The GL equation usually describes the optical soliton [8][9][10][11][12][13][14][15] propagation through optical fibers over longer distances.…”