Analysis of Malmquist-Takenaka-Christov rational approximations with applications to the nonlinear Benjamin equation

Abstract In the paper, we study approximation properties of Malmquist-Takenaka-Christov (MTC) system. We show that discrete MTC approximations converge rapidly under mild restrictions on functions asymptotic at infinity. This makes them particularly suitable for solving semi- and quasi-linear problems containing Fourier multipliers, whose symbols are not smooth origin. As a concrete application, provide rigorous convergence stability analyses collocation scheme nonlinear Benjamin equation. demonstrate method converges admits an efficient implementation, comparable to best spectral hybrid Fourier/finite-element methods described in literature.