PHYSICAL REVIEW 8 VOLUME 43, NUMBER 1 1 JANUARY 1991 Creation of sine-Gordon solitons by a pulse force Yuri S. Kivshar Institute for Low Temperature Physics and Engineering, 47 Lenin Auenue, 310164 Kharkou, US S R. . Boris A. Malomed P P. S. hirshou Institute of Oceanology, 23 Krasikov Street, 117234 Moscow, US. S.R Zhang Fei and Luis Vazquez Departamento de FI'sica Teorica, Facultad de Ciencias FI'sicas, Uni Uersidad Complutense, E-28040 Madrid, Spain (Received 22 May 1990) We study the problem of soliton generation by an external pulse force in the framework of the sine-Gordon system. The problem is applied to the creation of Auxons in long Josephson junctions or magnetic solitons in one-dimensional magnetic systems with an easy-plane anisotropy. In case of a small duration of driving pulse T, we find the connection between parameters of the pulse force and the wave field created after the pulse. To define the parameters of the generated soliton we use an approach based on the inverse scattering transform. The analytical results are presented in two cases when the spatial length L of the pulse is either much larger or much smaller than the value Vg T Vg being the maximum value of the group velocity in the system. The threshold conditions ad- mitting generation of either breathers or kink-antikink pairs are found. Numerical simulations are performed for arbitrary values of the ratio L/Vg T but for small T. In two limiting cases the results are in good comparison with the obtained analytical formulas. The influence of dissipative losses on the soliton creation is also studied by analytical and numerical methods. It is demonstrated that dissipation leads to an increasing of the threshold conditions to generate solitons by the pulse force. I. INTRODUCTION The concept of the soliton plays an important role in modern solid-state physics. Well-known examples are long Josephson junctions (LJJ's) and magnetic systems in- cluding ferromagnets and antiferromagnets. Theoretical models of both these systems reduce to the sine-Gordon (SG) equation. ' As is well known, this equation admits solitons of two distinct types: topological solitons (kinks) and nontopological ones (breathers). In the theory of LJJ's, a kink represents a Auxon, i.e. , magnetic fIux quan- tum. ' In the theory of one-dimensional magnetic sys- tems, a kink corresponds to a domain wall. An important physical problem is the generation of solitonic excitations in these systems. In LJJ s of the in- line type, Auxons are created by application of a bias current pulse to an edge of the junction. ' In LJJ's of the overlap type, they are created by application of the magnetic-field pulse. A spatially localized pulse of the magnetic field can also be employed to generate pairs of domain walls (DW's) and/or magnetic solitons (MS's) (breathers) in easy-plane ferromagnets. ' Unlike DW's, MS's are sufficiently dynamical excitations, and the problems of their nonthermal creation and stabilization are very im- portant from the viewpoint of recent experimental at- tempts to create and study the properties of the dynami- cal solitons in a few magnetic systems. The problem of soliton generation arises in any physi- cal system admitting existence of solitonic excitations, and it is not easy to solve. The exact analytical results may be obtained only for the Cauchy problem when the equation of motion can be solved by the inverse scatter- ing transform (IST). The IST method allows us to predict asymptotic evolution of an initial wave-field distribution defined at t =0, and, in particular, to calculate parame- ters of created solitary waves. In this connection it should be noted that a detailed analysis of some of the simplest initial SG wave-field configurations was carried out from the viewpoint of the IST in Refs. 11 and 12. Experimental conditions are associated with another situation, when an intense and generally localized pulse force drives a system from equilibrium, and the external pulse force results in a wave-field distribution from which solitons may be created. This clearly indicates that the parameters of the excited solitons are, in the final analysis, determined by the characteristics of the pulse force, i.e. , its intensity and duration. The way to solve such a problem was brieAy described by Kivshar and Malomed, ' ' and the method is based on the IST. In view of the fact that the formulation of the soliton generation problem most adequately corre- sponds to an experimental situation, we brieAy outline the general solution scheme. The problem of the linear response of a system to an external pulse acting during the time 0 & t & T is examined at the first stage, assuming that the system was in equilibrium [$=$, =0, where P(x, t) is the wave field] prior to the action of the external pulse force (t (0), and the spatial wave-field distribution at time t = T is also calculated. It is obvious that such a 43 1098 1991 The American Physical Society