sible to calculate the I - V characteristic (11) of the junc- tion. For the uniform current density distribution ( γ ( x ) = const) it has been shown that the relevant expressions for θ ( x ), ̂ ψ ( x ), and consequently the I - V dependence can be obtained in a closed fully analytical form (24). As fol- lows from Figs. 1 and 2, such an approximation is fairly accurate for moderate junction parameters. In general, however, practical FF oscillators are based on very long junctions with strongly nonuniform current profile. In such a case an analytical approximation (24) appears in- sufficient and one should look for a self-consistent solu- tion of Eqs. (10) and (18) which can be obtained by an iterative procedure. As shown in Figs. 1,2,4 and 5, the self-consistent so- lutions and numerical simulations are generally in very good agreement. The only exception, where one can ob- serve qualitative rather than quantitative agreement is the I - V curve shown in Fig. 4 for h = 2 . 5. As explained in the previous Section, the fluxon train is not dense enough for h = 2 . 5 and consequently the time-dependent part of the solution is periodic but not strictly sinusoidal, vio- lating the main assumption of the present approach. Finally, it should be mentioned that the method pre- sented here can be easily extended to include general, more realistic boundary conditions discussed in Refs. 16,17,27. In the present paper, however, we intention- ally assumed standard open-circuit boundary conditions (3), where the plasma waves could interfere after com- plete reflection at the boundaries, giving rise to clearly visible Fiske steps. This way, we were able to separate the influence of surface losses and self-pumping from that of boundary conditions, which (e.g. for a resistive load) can also affect the I - V characteristic and make the physical mechanism discussed here less clear. 7 Financial support from the Institute of Physics, Polish Academy od Sciences is gratefully acknowledged. Acknowledgments 1 T. Nagatsuma, K. Enpuku, F. Irie, and K. Yoshida, J. Appl. Phys. 54 , 3302 (1983); see also J. Appl. Phys. 56 , 3284 (1984); 58 , 441 (1985); 63 , 1130 (1988). 2 V. P. Koshelets, A. V. Shchukin, S. V. Shitov, and L. V. Filippenko, IEEE Trans. Appl. Supercond. 3 , 2524 (1993). 3 J. Mygind, V. P. Koshelets, A. V. Shchukin. S. V. Shitov, and I. L. Lapytskaya, IEEE Trans. Appl. Supercond. 5 , 2951 (1995). 4 V. P. Koshelets and S. V. Shitov, Supercond. Sci. Technol. 13 , R53 (2000). 5 V. P. Koshelets, S. V. Shitov, P. N. Dmitriev, A. B. Er- makov, L. V. Filippenko, V. V. Khodos, V. L. Vaks, A. M. Baryshev, P. R. Wesselius, and J. Mygind, Physica C 367 , 249 (2002). 6 M. Y. Torgashin, V. P. Koshelets, P. N. Dmitriev, A. B. Ermakov, L. V. Filippenko, and P. A. Yagoubov, IEEE Trans. Appl. Supercond. 17 , 379 (2007). 7 A. V. Khudchenko, V. P. Koshelets, P. N. Dmitriev, A. B. Ermakov, P. A. Yagoubov, and O. M. Pylypenko, Super- cond. Sci. Technol. 22 , 085012 (2009). 8 D. W. McLaughlin and A. C. Scott, Phys. Rev. A 18 , 1652 (1978). 9 P. S. Lomdahl, J. Stat. Phys. 39 , 551 (1985). 10 Yu. S. Kivshar and B. A. Malomed, Rev. Mod. Phys. 61 , 763 (1978). 11 M. Cirillo, N. Grønbech-Jensen, M. R. Samuelsen, M. Salerno, and G. Verona Rinati, Phys. Rev. B 58 , 12377 (1998). 12 M. Salerno and M. R. Samuelsen, Phys. Rev. B 61 , 99 (2000). 13 M. Jaworski, Phys. Rev. B 60 , 7484 (1999). 14 M. Jaworski, Supercond. Sci. Technol. 17 , 327 (2004). 15 A. L. Pankratov, Phys. Rev. B 66 , 134526 (2002). 16 A. S. Sobolev, A. L. Pankratov, and J. Mygind, Physica C 435 , 112 (2006). 17 A. L. Pankratov, A. S. Sobolev, V. P. Koshelets, and J. Mygind, Phys. Rev. B 75 , 184516 (2007). 18 M. Jaworski, Supercond. Sci. Technol. 21 , 065016 (2008). 19 J. R. Tucker and M. J. Feldman, Rev. Mod. Phys. 57 , 1055 (1985) 20 P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953). 21 M. Salerno and M. R. Samuelsen, Phys. Rev. B 59 , 14653 (1999). 22 M. Abramowitz and I.A. Stegun, Handbook of Mathemat- ical Functions (Dover, New York, 1982). 23 A. Barone and G. Paterno, Physics and Applications of the Josephson Effect (Wiley, New York, 1982). 24 K. K. Likharev, Dynamics of Josephson Junctions and Cir- cuits (Gordon and Breach, New York, 1986). 25 R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, Lon- don, 1982). 26 V. P. Koshelets, S. V. Shitov, A. V. Shchukin, L. V. Fil- ippenko, J. Mygind, and A. V. Ustinov, Phys. Rev. B 56 , 5572 (1997). 27 C. Soriano, G. Costabile, and R. D. Parmentier, Super- cond. Sci. Technol. 9 , 578 (1996).