Further physical study about solution structures for nonlinear q-deformed Sinh–Gordon equation along with bifurcation and chaotic behaviors

Abstract

In this article, with the help of Matlab R2021a software, the exact solutions of the nonlinear q-deformed Sinh-Gordon equation are successfully examined by ( G ′ G 2 )expansion method. The main novelty of this paper lies in five aspects: (1) To our best knowledge, the modified ( G ′ G 2 )expansion method was firstly applied in nonlinear q-deformed Sinh-Gordon equation (NQSGE). And thus get many new solutions that were not found previously literature [51,49].(2) The effects of wave obliqueness about NQSGE are firstly discussed in this paper which did not happen in previous papers [44,45,49,51,40]. (3) Phase portraits and bifurcation behaviors about NQSGE are also firstly investigated in Hamiltonian system that did not appear in previous literatures [44,45,49,51,40]. (4) Sensitive analysis to initial value and chaotic behavior are also firstly studied in NQSGE. This is also a work not done in other previous literatures [44,45,49,51,40]. (5) The modified Riemann-Liouville, Beta, Conformable and M-truncated fractional derivatives are tested for accuracy in Fig. 18 (a) and (b). To our best knowledge, we seem firstly compare the relations and distinctions among different fractional order derivatives in NQSGE model. The generalizations (1)-( 5) indicated the wave propagation of solitions about NQSGE model is mastered by the changed fraction, changed wave obliqueness angle and other