As the sun went down Wednesday on the vermilion walls and yellow tile roofs of Beijing's Forbidden City, the first families of the U.S. and China took in a Peking opera performance in the palace where China's emperors lived for nearly six centuries.

It was the start of what China's ambassador to the U.S. calls a "state visit plus" – a highly choreographed blend of stagecraft and statecraft, designed to highlight the evolving chemistry between Presidents Trump and Xi Jinping.

"China is receiving Trump almost the way the King of Saudi Arabia did," observes Shi Yinhong, an international relations expert at People's University in Beijing. China is "giving Trump lots of face, vanities and protocol."

Lavishing the "imperial treatment" on Trump and giving him the chance to bond with a fellow self-styled political strongman is just one way in which China is dealing with the U.S. president's potential disruptions to one of the world's most consequential bilateral relationships.

"I think we can say that so far, our measures have been relatively successful," comments Wu Xinbo with the Center for American Studies at Fudan University in Shanghai. At least, he notes, the two countries' presidents "have established a good working relationship."

That relationship did not get off to a smooth start. Trump threatened to upgrade relations with Taiwan, upending decades of the so-called "One China" policy. He also threatened to punish China for manipulating the value of its currency. But so far, none of that has happened.

Cui Liru of the China Institutes of Contemporary International Relations,a government think tank in Beijing, says that China handled these challenges the right way — by doing nothing at all.

"China had to realize that Trump needed to learn about China," he says, "and during this learning process, we had to stay cool and patient."

Cui says China judged that Trump was not really interested in changing the status quo among China, the U.S. and Taiwan. He merely wanted to use Taiwan as a bargaining chip to get better terms of trade with China.

On the currency manipulation issue, Cui says, it was just a matter of apprising Trump of the widely accepted fact that China was propping up the value of its currency, not depressing it.

Cui says another thing China had to do was "find a channel through which to communicate with Trump."

They found one such channel in his son-in-law Jared Kushner, who helped arrange an April summit between Xi and Trump at Trump's Mar-A-Lago resort in Florida.

That channel has apparently outlived its usefulness, as Kushner came under investigation in the Russian influence scandal and labor activists alleged abuses at a Chinese shoe factory making footwear for Ivanka's fashion label.

Xi and Trump have now met in person twice and spoken by phone nine times, and Trump has even praised Xi as a "very good man."

But Fudan University's Wu says Beijing is still unsure about whom to talk to in Washington.

"We still don't know who's involved in making China policy," he says. "Take Secretary of State Rex Tillerson, for example. It seems like he's not in the loop, or at least not in the inner circle."

Meanwhile, Beijing has made some concessions to Trump on trade — for example, increasing imports from the U.S. But Tsinghua University professor Chu Shulong argues that these were things China wanted anyway.

"China needs to import U.S. agricultural goods, airplanes and other products," he says. "China would also like to import some hi-tech items, but the U.S. doesn't want to sell us those."

Chu points out that every U.S. administration in recent decades has complained about China's trade surplus, violation of intellectual property and lack of market access.

"It's just that Trump uses somewhat stronger words," he says.

Since Trump took office, China has also tightened sanctions on North Korea, especially squeezing energy, banking and labor exchanges with its neighbor.

And that, says People's University's Shi Yinhong, is about as much as China can or is willing to do for now.

"China has nearly exhausted its leverage over North Korea," he says, "and the North is becoming increasingly hostile towards us."

Despite the friendly personal relations, the Trump administration has recently outlined its vision of a U.S. alliance focusing on what it calls "a free and open Indo-Pacific" region — the region better known up to now as the Asia-Pacific.

To China, that sounds like a repackaged Cold War-era policy to contain it.

Meanwhile, Tsinghua University's Chu notes that the U.S. and Chinese navies are bumping into each other with increasing frequency in contested waters of the South China Sea.

In 2001, a Chinese fighter jet collided with a U.S. spy plane, resulting in the death of the Chinese pilot and the detention of an American crew. Since then, the two sides have worked out protocols to keep such encounters from spiraling into another confrontation or crisis, but Chu still worries.

"Who knows when the two countries' warships might get too close or collide," he says, "or make some sort of miscalculation?"

For now, Chu says he's cautiously optimistic about Trump and Xi's personal relationship.

"But this could all change," he cautions. "Leaders have to put the national interest and their own agenda first, and not personal relationships."

Chu points out that President Obama started out pretty bullish on China, but by his second term, he'd largely soured on it. And Trump himself has at times also expressed disappointment with China.

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