Abstract. The constant pressure free-inflation test is a very versatile and simple tool for analyzing different features of superplastic forming. In recent years, methods have been proposed to measure constitutive parameters the stress–strain relationship material, specifically K m power law model. However, this restricted be used in narrow strain-rate ranges, poor results are obtained when app...

We report on the possibility of unidirectional motion of a topological soliton in a dissipative AC-driven sine-Gordon equation. This motion is due to breaking of certain space-time symmetries. It can be achieved by the proper choice of the potential or the AC force. We formulate the necessary symmetry conditions for the AC force and confirm them with the first order perturbation theory and nume...

With the help of computer symbolic computation software e.g., Maple , abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equati...

We study relations of the Weierstrass’s hyperelliptic al-functions over a non-degenerated hyperelliptic curve y = f(x) of arbitrary genus g as solutions of sine-Gordon equation using Weierstrass’s local parameters, which are characterized by two ramified points. Though the hyperelliptic solutions of the sine-Gordon equation had already obtained, our derivations of them is simple; they need only...

We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex MongeAmpère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Mo...

We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex MongeAmpère equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Mo...

We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modi-ed Korteweg{de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectr...