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We consider the interaction of solitary waves in a model involving thewell-known $\phi^4$ Klein-Gordon theory, but now bearing both Laplacian andbiharmonic terms with different prefactors. As a result of the competition ofthe respective linear operators, we obtain three distinct cases as we vary themodel parameters. In the first the biharmonic effect dominates, yielding anoscillatory inter-wave interaction; in the third the harmonic effect prevailsyielding exponential interactions, while we find an intriguing linearlymodulated exponential effect in the critical second case, separating the abovetwo regimes. For each case, we calculate the force between the kink andantikink when initially separated with sufficient distance. Being able to writethe acceleration as a function of the separation distance, and itscorresponding ordinary differential equation, we test the correspondingpredictions, finding very good agreement, where appropriate, with thecorresponding partial differential equation results. Where the two findingsdiffer, we explain the source of disparities. Finally, we offer a first glimpseof the interplay of harmonic and biharmonic effects on the results ofkink-antikink collisions and the corresponding single- and multi-bouncewindows.

Kink-Antikink Interaction Forces and Bound States in a $\phi^4$ Model with Quadratic and Quartic dispersion