Jacobi elliptic function solutions of the double dispersive equation in the Murnaghan's rod

Analyzing nonlocal nonlinear vibrations of two-phase geometrically imperfect piezo-magnetic beams considering piezoelectric reinforcement scheme

“…Also, the elliptic function frequency has been denoted by ω . The Jacobi elliptic function ( cn ) can be written in series of trigonometric form as a function of complete elliptic integral of the first kind K ( k ) as 33,34…”

“…where q = exp ( − π K ′ / K ) and K ′ = K ( l ) denotes the associated complete elliptic integral of the first kind. 33,34…”

“…where q ¼ expðÀpK 0 =KÞ and K 0 ¼ KðlÞ denotes the associated complete elliptic integral of the first kind. 33,34 Then, inserting equation (74) into equation (75) and with the use of series expansion for cn cn j j'a 0 cn + a 1 cn 3 , one can express that…”

Some newly explored exact solitary wave solutions to nonlinear inhomogeneous Murnaghan’s rod equation of fractional order

“…Cattani et al [36] had used extended Sinh-Gordon equation expansion method (ShGEEM) and the modified exp(−φ(ζ ))expansion function method, to find different types of solitary wave solutions. Moreover, Baskonus et al [37] solved inhomogeneous Murnaghan's rod by Fexpansion method and obtained Jacobi elliptic function solutions including bright and dark solitons, topological, non-topological, singular, periodic, their combinations and compound solitons.…”

Düzenli Uzun Dalga Denkleminin Hiperbolik Tip Yürüyen Dalga Çözümleri

“…Variety methods have been used to find the analytical solutions of such equations (NLDEs). Some of these are F-expansion technique [1], Laplace transform method [2],   1 G expansion method [3][4][5], the residual power series method [6,7], modified exp -expansion function method [8][9][10],…”