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We investigate the structure of solutions of boundary value problems for aone-dimensional nonlinear system of pseudodifferential equations describing thedynamics (rolling) of p-adic open, closed, and open-closed strings for a scalartachyon field using the method of successive approximations. For an open-closedstring, we prove that the method converges for odd values of p of the formp=4n+1 under the condition that the solution for the closed string is known.For p=2, we discuss the questions of the existence and the nonexistence ofsolutions of boundary value problems and indicate the possibility ofdiscontinuous solutions appearing.

Nonlinear equations for p-adic open, closed, and open-closed strings