Hitherto, the bilinear transformation method has been used to obtain analytic solutions of completely integrable (or nonlinear evolution) equations. In this first of two studies (designated I and II), it is shown that the method may apply equally well to those nonlinear wave equations dubbed partially integrable. Here the regularized long‐wave (RLW) and RLW Boussinesq (RLWB) equations are considered as examples. In each case, the bilinear form is found to have an ‘‘extra’’ equation which would appear to signal their nonintegrability. Their solitary‐wave solutions are reconstructed and the nonexistence of multisoliton solutions is demonstrated. The present work provides the basis for the construction of periodic solutions in II.
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