Multi‐Rogue Wave, Generalized Breathers Wave, Bell Shape and Singular Wave Solutions to the (3 + 1)‐Dimensional Yu‐Toda‐Sasa‐Fukuyama Equation

ABSTRACT The (3 + 1)‐dimensional Yu‐Toda‐Sasa‐Fukuyama equation (YTSFe) is explored in this work. Applying traveling wave transformation, the (3 + 1)‐dimensional YTSFe is reduced into the (1 + 1)‐dimensional model. Then, upon the Hirota bilinear equation that is developed through the Cole‐Hopf transformation, the multi‐rogue wave solutions of the first‐ and second‐order type are investigated via introducing the different polynomial functions. In addition, the generalized breathers wave solutions are explored through the new homoclinic approach. In the end, the bell shape and singular wave solutions are also probed by taking the exponential function as the test function. Correspondingly, the dynamic attributes of the extracted exact wave solutions are unfolded by means of the Maple. To the best of the author's knowledge, the relevant results explored in this work are all new and have not been reported till now.