Reciprocal Bäcklund transformations and travelling wave structures of some nonlinear pseudo-parabolic equations

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

“…Now, we need to solve only equation (10) first. After balancing the highest order derivative terms with the nonlinear terms appearing in equation (10), one can take the solution of the form:…”

“…After plugging equation (12) into equation (10) and equating coefficients of various powers of ( ) r , we get a system of algebraic equations as given below:…”

“…Finding solutions to nonlinear problems is a difficult task. Several approaches have been suggested, including the improved F-expansion method [7], the variational iteration method [8], the inverse scattering technique [9], the tanh-coth function technique [10], the Jacobi elliptic function expansion technique [11,12] and disciplines, and opened up new avenues. Many of the techniques created for the analysis of NLPDEs exhibit a level of sophistication that makes it challenging for many researchers to access them [14][15][16][17][18].…”

Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system

“…The objective of this research is to showcase results and recent developments in the theory of evolution equations, encompassing both theoretical and practical aspects. Many researchers and mathematicians have suggested a variety of efficient methods 1 – 6 for finding exact solutions of nonlinear (NPDEs), such as Hirota’s bilinear method 7 , tanh function method 8 , the inverse scattering technique 9 , the Bäcklund transformation method 10 , modified variational iteration method 11 , the multiple exp-function approaches 12 , the Darboux transformation approach 13 , the Lie symmetry analysis 14 – 16 , the -expansion approach 17 , the Kudryashov technique 18 and the Jacobi elliptic technique 19 – 21 .…”

Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

“…Lie group methods [20][21][22][23][24][25][26][27][28] mainly deal with the nonlinear PDEs to furnish the exact solutions. This technique was initiated by Sophus Lie [29,30] and then followed by Ovsyannikov [31], Ibragimov [32], Bluman [33] and Hydon [34].…”