Chaotic behavior and traveling wave solutions of the fractional stochastic Zakharov system with multiplicative noise in the Stratonovich sense

Bifurcation, chaotic pattern and traveling wave solutions for the fractional Bogoyavlenskii equation with multiplicative noise

“…Consequently, the research findings in this paper hold significant value for both theory and practice. In contrast to the latest literature [16], this article not only obtains the dynamic behavior of FSBE (1.1), but also provides new traveling wave solutions. This article, for example, found solutions for exponential functions, hyperbolic functions, and elliptic functions such as U 1,1 , U 1,2 , U 1,3 , U 1,6 , U 2,1 , U 2,2 and so on.…”

“…This article, for example, found solutions for exponential functions, hyperbolic functions, and elliptic functions such as U 1,1 , U 1,2 , U 1,3 , U 1,6 , U 2,1 , U 2,2 and so on. This paper's novelty is seen in the absence of these solutions in [16].…”

“…So many cases or experiments have found that the random factor is long-lasting memory and independent incremental, and therefore SPDEs driven by the Brownian motion are among the most effective methods to describe such a phenomenon [13,14]. In view of the importance of theory and practice, the dynamic behavior of fractional order Stochastic differential equation has always been an important research topic [15,16].…”

Nonlinear complex generalized zakharov dynamical system inconformal sense utilizing new kudryashov method

“…Considering the rapid growth of symbolic computation systems, soliton solutions make it possible to analyze nonlinear physical phenomena; thus, examination of the soliton solutions for NLPDE has recently attracted the attention of researchers [1,2]. In the literature, there are diverse approaches applied by researchers to produce analytical solutions of NLPDE such as the first integral method [3,4], the extended Kudryashov technique [5], the Riccati Bernoulli sub-ODE scheme [6,7], the modified simple equation scheme [8], the extended rational sine-cosine and sinh-cosh method [9], the extended Poincare-Lighthill-Kuo method [10], the extended simplest equation method [11], traveling wave solution [12], the auxiliary ordinary differential equation method and the generalized Riccati method [13], the solitary wave solution technique with the…”