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**Sample text**

P. Pitaevskii, Theory of Solitons: Method of the Inverse Problem [in Russian], Nauka, Moscow (1980). V. E. Zakharov and A. V. Mikhailov, "Relativistically invariant two-dimensional models of field theory integrable by the method of the inverse problem," Zh. Eksp. Teor. , 7_44, No. 6, 1953-1974 (1978). V. E. Zakharov and A. B. Shabat, "Integration of nonlinear equations of mathematical physics by the method of the inverse scattering problem. II," Funkts. Anal. , 13, No. 3, 13-22 (1979). V. E. Zakharov and A.

We shall prove the last assertion of the theorem. Suppose that q ~ I. 81 LEMMA 3 . 1 . 18) E, P r o o f . As in the p r o o f of t h e c o r o l l a r y of Theorem 2 . 39) a r e c o n n e c t e d w i t h the f i r s t v a r i a t i o n s 6 I j . Hence, by Eqs. ( 3 . 16) we have -~0. 19) 821. 19), we obtain the assertion of the lemma. Since at minima all A(e) must be positive while P(E) changes sign on passing across a forbidden zone, the second term must also change sign (if the contour of integration does not intersect this zone).

67. 68. 69. 90 I. V. Cherednik, "On solutions of algebraic type of asymmetric differential equations," Funkts. Anal. , 15, No. 3, 93-94 (1981). M. A. Ablowitz, D. J. Kaup, A. S. Newell, and H. Segur, "Method for solving the sineGordon equation," Phys. Rev. , 30, 1262-1264 (1973). S. Aubry, "Analytlcity breaking and Anderson localization in incommensurate lattices," Ann. Israel Phys. , ~, 133-164 (1980). S. Aubry, "Metal--insulator transition in one-dimensional deformable lattices," Bifurcation Phenomena in Math.