We study a family of classical string solutions with large spins on Rt×S subspace of AdS5×S background. These solutions are related to Complex sine-Gordon solitons via Pohlmeyer’s reduction. The equations of motion for the classical strings are cast into Lamé equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the close...

where u = u(t, x) ∈ C(R,R) and V (x) ∈ C(R,R), by using the method of separation of variables (SV). Equations belonging to class (1) are widely used in the modern quantum physics and can be related to other linear and nonlinear equations of mathematical physics (these relations will be discussed below, at the end of the article). In particular, class (1) contains the d’Alembert equation (with V...

We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove localin-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that class...

A nonlinear chain driven by one end may propagate energy in the forbidden band gap by means of nonlinear modes. For harmonic driving at a given frequency, the process occurs at a threshold amplitude by sudden large energy flow that we call nonlinear supratransmission. The bifurcation of energy transmission is demonstrated numerically and experimentally on the chain of coupled pendula (sine-Gord...

We show that the Klein-Gordon equation on the quaternion field is equivalent to a pair of DKP equations. We shall also prove that this pair of DKP equations can be taken back to a pair of new KG equations. We shall emphasize the important difference between the standard and the new KG equations. We also present some qualitative arguments, concerning the possibility of interpreting anomalous sol...

This article presents a new iterative method (NIM) for the investigation of approximate solution Klein-Gordon and sine-Gordon equations. approach is formulated on combination Mohand transform homotopy perturbation method. (MT) capable to handle linear terms only, thus we introduce (HPM) tackle nonlinear terms. NIM derives results in form series solution. The proposed emphasizes stability derive...

This is a comment on a reply to a comment on a paper of Hellaby & Dray, repeating the identification of an important mistake which is still being denied by the authors: their proposed solutions do not satisfy the Einstein-Klein-Gordon equations at a change of signature. Substitution of the proposed solutions into the Einstein-Klein-Gordon equations in unit normal coordinates yields Dirac δ term...

An useful strategy for the study of nonlinear partial differential equations (PDE) arising in pattern formation is to consider asymptotic solutions containing one or several localized defects and to simplify the dynamics by finding the equations of motion of the system of interacting defects. The great advantage of this approach is that we are dealing with ordinary differential equations (ODEs)...

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gor...