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1991 Mathematics Subject adjacent saddle Anal analytic continuation approximation arg(z assume Assumption asymptotic behavior asymptotic expansion back waves blow-up boundary conditions boundary layer boundary-value problem coefficients consider convergence corresponding curve defined denote derived differential equations Dirichlet eigenvalue entire function estimates exists exponential type follows formula function of exponential given Hence holds i(Ea implies incomplete gamma functions inequality integral equations integral representations interval Jacobi polynomials Lemma linear Math Mathematics Subject Classification method Mimura Neumann Neumann boundary conditions nonlinear nonnegative obtain Olver ordinary differential equations orthogonal polynomials oscillation oscillatory P-pulse paper parameter positive constant proof of Theorem properties prove pulse waves respect saddle point satisfies second-order Section sequence SIAM singular limit singularly perturbed solitary wave space stability Stokes line sufficiently small Theorem 3.1 transform traveling front traveling pulse uniformly values variable vector Wong zero