Primitive potentials and bounded solutions of the KdV equation

Gardner, 1967, Method for solving the Korteweg de Vries equation, Phys. Rev. Lett., 19, 1095, 10.1103/PhysRevLett.19.1095 Lax, 1968, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math., 21, 467, 10.1002/cpa.3160210503 Novikov, 1974, The periodic problem for the Korteweg–de Vries equation, Funct. Anal. Appl., 8, 236, 10.1007/BF01075697 Its, 1975, Hill’s operatos with a finite number of lacunae, Funct. Anal. Appl., 9, 65, 10.1007/BF01078185 Its, 1975, Hill’s operatos with a finite number of lacunae and multisoliton solutions of the KdV equation, Theoret. Math. Phys., 23, 343, 10.1007/BF01038218 Novikov, 1984 Zakharov, 2009, Turbulence in integrable systems, Stud. Appl. Math., 122, 219, 10.1111/j.1467-9590.2009.00430.x Marchenko, 1988, Vol. 17 Lundina, 1990, Compactness of sets of reflectionless potentials, J. Soviet Math., 48, 290, 10.1007/BF01101248 Marchenko, 1991, The Cauchy problem for the KdV equation with non-decreasing initial data Bargmann, 1949, On the connection between phase shifts and scattering potential, Rev. Modern Phys., 21, 488, 10.1103/RevModPhys.21.488 Zakharov, 1985, Construction of higher-dimensional nonlinear integrable systems and of their solutions, Funct. Anal. Appl., 19, 89, 10.1007/BF01078388 Shabat, 1970, About reflectionless potentials, in the coll, Dinamika Sploshn. Sredy, 5, 130 I. Krichever, Private communication. Zakharov, 1971, Kinetic equation for solitons, Sov. Phys.—JETP, 33, 538 El, 2005, Kinetic equation for a dense soliton gas, Phys. Rev. Lett., 95, 10.1103/PhysRevLett.95.204101